Akuna Options 101 PDF

Akuna Options 101 Authors Akuna Capital Status Done tags finance options Section 1 1.1: Terminology and Trading Floors Akuna Options 101 1  📓 General Marke...

Akuna Options 101 Authors Akuna Capital Status Done tags finance options Section 1 1.1: Terminology and Trading Floors Akuna Options 101 1  📓 General Market Making Definitions: Bid: Highest price for which someone is willing to buy something Ask/Offer: Lowest price for which someone is willing to sell something Size/Lots: # of contracts one is willing to trade at a price Make a market: To provide a bid ask price and sizes for each e.g. 60 bid for 4 and have 10 at 68 (notice, giving a bid follows PRICE for SIZE and showing an ask follows SIZE at PRICE) Spread: Ask - Bid Hedge: A trade to reduce the risk of price movement in an asset. Paper: The interested parties trading against you Broker: A perosn or company that acts as an intermediary between buyers and sellers Tick Size: Smallest increment between one level and the next level (e.g. 1 cent or 1/8th of a cent) Queue Priority: A structure used to determine the right of precedence between those in a list e.g.: Price-Time Priority - Exchange orders the order book by price and then by whoever entered their order earliest Bid: Highest price for which someone is willing to buy something Ask/Offer: Lowest price for which someone is willing to sell something Size/Lots: # of contracts one is willing to trade at a price Make a market: To provide a bid ask price and sizes for each e.g. 60 bid for 4 and have 10 at 68 (notice, giving a bid follows PRICE for SIZE and showing an ask follows SIZE at PRICE) Spread: Ask - Bid Hedge: A trade to reduce the risk of price movement in an asset. Paper: The interested parties trading against you Akuna Options 101 2  Broker: A perosn or company that acts as an intermediry between buyers and sellers Tick Size: Smalles increment between one level and the next level (e.g. 1 cent or 1/8th of a cent) Queue Priority: A structure used to determine the right of precedence between those in a list e.g.: Price-Time Priority - Exchange orders the order book by price and then by whoever entered their order earliest e.g. 60 bid for 4 and have 10 at 68 (notice, giving a bid follows PRICE for SIZE and showing an ask follows SIZE at PRICE) e.g.: Price-Time Priority - Exchange orders the order book by price and then by whoever entered their order earliest Akuna Options 101 3  📚 Order Types Immediate or Cancel (IOC)/Fill-and-Kill (FAK): A type of order that requires all or part of the order to be executed immediately. Unfilled parts of the order are cancelled Good for Day (GFD): A type of order that will reamin active until executed (in part or full) or until the end of the trading day. Then cancelled. Good-Til-Cancelled (GTC): A type of order that will remain active until completed or cancelled. All-or-None (AON): A type of order that must be executed in its entirety, or not executed at all. Fill-or-Kill (FOK): A type of order that must be executed immediate in its entirety or is otherwise cancelled. One-cancels-the-other (OCO): When one order or market is executed, the other order is automatically cancelled. Immediate or Cancel (IOC)/Fill-and-Kill (FAK): A type of order that requires all or part of te order to be executed immediately. Unfilled parts of the order are cancelled Good for Day (GFD): A type of order that will reamin active until executed (in part or full) or until the end of the trading day. Then cancelled. Good-Til-Cancelled (GTC): A type of order that will remain active until completed or cancelled. All-or-None (AON): A type of order that must be executed in its entirety, or not executed at all. Fill-or-Kill (FOK): A type of order that must be executed immediate in its entirety or is otherwise cancelled. One-cancels-the-other (OCO): When one order or market is executed, the other order is automatically cancelled. Akuna Options 101 4  📚 Option Specific Terms Settlement Time: The specific time of days options expire and futures “settle” for the day. Contract Size: The multipler attached to an option or future. Options on stocks generally have a multipler of 100 shares. Options on futures have a multiplier of 1 future. Vol bid, catching a bid, ripping/exploding: Variety of terms for vol going up. Vol offered, vol smashed/smoked: Variety of terms for vol going down. Teenie: lowest priced options. genearlly traded for movement risk purposes. Theo: Theoretical fair value for something Liquidity: How easy/hard it is to trade close to fair value. Generally determiend by the number of contracts on the bid/ask along with the width of the market (how deep the bid and asks are) Settlement Time: The specific time of days options expire and futures “settle” for the day. Contract Size: The multipler attached to an option or future. Options on stocks generally have a multipler of 100 shares. Options on futures have a multiplier of 1 future. Bid offset: edge needed around theo to auto-trade the option Quote bid offset: edge needed around theo to quote an option 1.2: How Do Market Makers Profit Ans: Collecting spread, scalping Akuna Options 101 5  How can you sell something you don’t own? Options are contracts unlike some physical underlying thing (for example, shorting a stock requires you to borrow someone else’s stock and pay a borrow fee). Instead, buying or selling an option is simply choosing which side of the contract you want to be on. Settling an option: Stock Option: deliver or buy the underlying shares of stock which you will need to borrow or locate Cash Settled Option: Pay the buyer cash between strike and settlement. Examples: Lean HOgs, Feeder Cattle and some Nat Gas futures Examples: Lean HOgs, Feeder Cattle and some Nat Gas futures Future Settled Option; Deliver a future Physical Delivery (Futures): Physically delivering the underlying asset to the buyer. Marketplaces: Either electronic exchanges/screen trading or open outcry floors/trading pits Examples: CME Group COMEX: metals NYMEX: energy (oil, gas) CBOT: grains and treasuries CME: currencies, Eurodollars, SP500, livestock Examples: ICE Brent & WTI Oil, sugar, coffee, cocoa, orange juice pulp, Russell indices, USD index Examples: CBOE The only exchange to trade the SPX index and VIX options (due to licensing agreements) Examples: CME Group Akuna Options 101 6  COMEX: metals NYMEX: energy (oil, gas) CBOT: grains and treasuries CME: currencies, Eurodollars, SP500, livestock Examples: ICE Brent & WTI Oil, sugar, coffee, cocoa, orange juice pulp, Russell indices, USD index Examples: CBOE The only exchange to trade the SPX index and VIX options (due to licensing agreements) COMEX: metals NYMEX: energy (oil, gas) CBOT: grains and treasuries CME: currencies, Eurodollars, SP500, livestock Brent & WTI Oil, sugar, coffee, cocoa, orange juice pulp, Russell indices, USD index The only exchange to trade the SPX index and VIX options (due to licensing agreements) Over-the-Counter (OTC): Trades that happen ‘off-floor’ and are directly transacted between two parties. Much more counterparty risk trading OTC since there is nothing ensuring that the counterparty will honor their trade or has the funds/credit to back the deal if it goes bad 1.3 Understanding Different Assets: Stock: A share in a company that has access to some cash flow that the company produces. Issued to rasise capital Future: A contract between two parties to buy/sell a commodity or asset at a predetermined price at a specified time in the future. Buyer (consumer) is taking Akuna Options 101 7  on the obligation to buy the underlyhing when the future expires. Seller (producer) has the obligation to provide the underlying asset at that date. Forward: Exact same as a future but a future trades on an exchange while a forward is an OTC product Options: Derivative Insturment because it’s contract is derived from an underlying asset Call Option: The right but not the obligation to buy the underlying at a specificed price (strike price) on or before a specific date. Put Option: The right but not the obligation to sell the underlying at a specificed price on or before a specific date. Multiplers: Unlike in stocks, different insturments such as options represent a different multiple of underlying. E.g. corn futures represetn 5000 bushels of corn. Question: As strikes go up, how should the prices of calls and puts change? Ans: Theo of a call goes down and theo of a put goes up Question: Consider the following image Why are the last traded prices for calls and puts for at the money options roughly the same? Ans: When you are at the money, its basically a coin toss as to where to whether the stock goes up or down so payout for the call and puts are about the same. Hence they have the same price Akuna Options 101 8  1.4: Types of Options Combos 📚 Examples Long Call Spread (cs): Buy call and short call such that short has a higher strike than long. Same expiry. Long Put Spread (ps): Buy put and short put such that the short has a lower strike than the long. Same expiry Box: A cs + ps Straddle: To go long/short both the call and put with same strike and expiration. Straddles are bets are volatility since being long the straddle implies that one believes the underlying is going to move a certain perctange before expiration. Strangle: Similar to the straddle but the calls and puts have different strikes. Going long strangles costs a smaller options premium but require greater volatility to be profitable. Butterfly: The long call butterfly is to go short two calls at a middle strike and long a call at an upper strike and long a call at a lower strike. All calls have the same expiry date. Ratio Spread (1x2 cs or 1x2 ps): Similar to cs and ps but you double up on the higher strike. I.e., for a long cs, buy 1 call at the lower strike and sell 2 calls at the higher strike. Risk Reversal (rr): Buying lower strike put vs selling higher strike call Reversal/conversion (rr): A reversal is buying the call and selling the put on the same strike and selling the underlying. A conversion is simply the reverse Section 2 Akuna Options 101 9  2.1: Payoff Diagrams Payoff diagrams show the profit of an option or multiple option combination (called spreads or combos) at expiry for various underlying prices. Akuna Options 101 10  📓 Examples Basic Options Strategies: Speculative Strategies: Akuna Options 101 11  Covered Calls: Suppose we are long the market and we want to hedge a little and cap our upside. We can sell a call at a strike K which will collect a premium and cap our upside if the underlying goes above K. Protective Put: We buy a put and buy the underlying that caps your downside and shifts your breakeven point up by the premium of the put. Long calls are a cheaper way to express the belief that underlying will go up Volatility Strategies: Straddles and flys are ways to express a belief on volatility of underlying. 2.2: Time Premium and Put-Call-Parity 📚 Time Premium In-the-Money (ITM): If given the option for free, it would instantly make money from its inherent value. For example, an ITM call means that the strike is less than the current underlying price. Out-of-the-Money (OTM): Option has no intrinsic value. For OTM calls, strike greater than current underlying price. At-the-Money (ATM): Strike = Underlying Price Intrinsic Value: Portion of the option price attributed to the difference between the current underlying price and the strike Extrinsic Value (Time Premium): Portion of option attributed to the optionality of the option itself. OTM has only extrinsic value while ITM have both intrinsic and extrinsic value. What factors influence the extrinsic value of an option? Def: A forward contract is a contract between two parties to buy/sell an asset at a specified future time at a strike price. Akuna Options 101 12  First, we establish a forward price which is the price of the underlying at a future time (the option expiry). This price accounts for the 1) current price of the underlying or “spot price” 2) interest rates 3) dividends if applicable 4) carrying costs if applicable. Once a forward price is established, the factors that contribute to extrinsic value are: Distance to ATM: How far the strike is from the forward. Time: time to expiry. A 1 year option will cost more than a 6 month option all else being equal since it has more optionality Volatility: Higher implied vol will lead to higher option prices. Put Call Parity (PCP) Simplified Put-Call-Parity: The value of an ITM option is equal to its intrinsic value plus the value of the corresponding OTM option, representing the extrinsic value. Call Price - Put Price = Underlying Price - Strike or C - P = U - K If this formula does not hold, arbitrage exists. Namely, if C - P > U - K, we short the call and long the put and similarly if C - P < U - K. Intuitively, PCP explains the observation that being long a call and short a put with the same strike is essentially the same as being long the underlying instrument (consider the payoff diagrams of that combo, i.e. imagine flipping one of the legs of a straddle) Long Call + Short Put = Long Forward. Hence, Long Call + Short Put - Long Forward = 0 Credits: Earn selling put (P), earn selling forward/underlying (U) Debits: Lose buying call (C), lose buying strike(K, either buying oil back at strike price since you exercise your call or the put you sold is exercised) P + U = C - K, another formulation of PCP Note, we are selling and buying the calls, puts, and forward right now and buying the strike and expiry. Thus, we are actually earning/losing interest Akuna Options 101 13  on these trades: Credits: P * exp(rt) + U * exp(rt) Debits: Call * exp(rt) + K Forward = (C - P)exp(rt) + K 2.4: Option Limits/Boundaries 📚 Options Relationships These relationships always hold and allow traders to sense check their systems and spot opportunities: An ITM call or put should never be worth less than its intrinsic value An option can never be worth less than zero. A call spread can never be worth more than the difference between the strikes A symmetrical fly should never be worth less than zero. A same-strike calendar (expiring into the same underlying) can never be worth less than 0. The further month offers more optionality than the closer month. PCP always holds Akuna Options 101 14  📚 Exercise: Spreads and Flies What is the current theoretical value of the 380/400 cs? Cost of cs is -11.750 + 5.875 = -5.875. Theo is 11.67 - 5.92 = 5.75 What is the current theoretical value of the 400/420/440 call fly? asdf What are the lower and upper bounds for the above call fly? What is an estimate for the current forward price of the underlying? Akuna Options 101 15  📚 Exercise: Theo and PNL Calc Below is an outright options screen for July Corn options. The underlying is a September Corn future (current market in future is shown in top part of window as 649.00 at 651.00). Our theoretical option prices (theos) are based on the future mid-price of 650.00 from this bid/ask market. Corn has a multiplier of 5,000 and is quoted in pennies. So 1 option displayed as 0.01 = 0.0001 pennies, which is 0.01 * 50 = 0.0001 * 5000 = $0.50 notional value. Corn options trade in 1/8th tick increments (.125). Akuna Options 101 16  Calculate the theo, edge and/or cash edge (P&L) for each of the questions given, assuming we trade each option or spread 100 times. Buy 620/570 put spread for 11.75, 1x. What is the theoretical value and cash edge of the spread? 12.03, $1400 Akuna Options 101 17  Buy the 710 put for 63.00. What is the edge and cash edge of the trade? 8.42, $42,100 Sell 500 call at 151.00. What is the theoretical value of the call, and the edge of the trade? 150.51, 0.49 Buy 500/670 strangle for 23.25. What is the edge and the cash edge of the strangle? 0.44, $2,200 Buy the 670 put for 22.17. What is the edge and cash edge of the trade? 21.10, $105,500 Section 3: The Greeks Greeks are partial derivative of the option price wrt some different important variables. Greeks describe the characteristics and dimensions of risk associated with an option position. The 5 main greeks are, Delta, Gamma, Theta, Vega, and Rho. 3.1: Delta Akuna Options 101 18  📚 Definition: 1. The delta of an option is the partial derivative of price wrt to underlying price. 2. Hedge ratio. Delta is thus the number of underlying contracts that allows one to establish a neutral hedge under current market conditions using the current theoretical value of an option. 3. Probability that the option will expire ITM. E.g. a 40 delta call has roughly a 40% chance of finishing ITM. Its corresponding put must have a 60% chance. Call options are assigned a delta between 0 and 1.00 (for each +1 change in underlying, how much does call option price change) but traders commonly drop the decimal and express delta between 0 and 100 When you buy (sell) a call your delta will be a positive (negative) number. When the underlying increases in price, the value of the call will increase by the option’s delta multiplied by the change in underlying price. Conversely, when the underlying decreases in price the value of the call will decrease by the delta value multiplied by the change in underlying price. Note, this only holds for relatively small underlying moves, as we’ll discuss in the gamma section. Put options will have a delta between -1 and 0 (-100 and 0). When the underlying increases, put values decrease. Holding the correct delta ratio position in the underlying will offset any option gains/losses. Delta is dynamic: 1. How does delta change wrt to implied volatility: a. OTM Calls: Increased implied vol = delta approaches +0.5, Decreased IV = delta approaches 0 Akuna Options 101 19  i. Approaches 0.5 because at infinite implied vol, the OTM will finish ITM with a 50/50 chance b. ITM Puts: Increased implied vol = delta approaches -0.5, Decreased IV = delta approaches -1 2. Delta wrt to time to expiry: a. OTM Calls: Increases time to expiry = delta approaches +0.5, Decreased IV = delta approahces 0 b. ITM Puts: Increases time to expiry = delta approaches -0.5, Decreased IV = delta approaches -1 c. Notice: Increase in time ~ increase in implied vol 3. Delta wrt to strike: a. Calls: Increasing call strikes decreases delta b. Puts: Increasing call strikes = delta approaches towards -1 3.2: Gamma 💡 Definition: Gamma is the rate at which delta changes with changes in the underlying. That is, the change in delta per 1 point move in the underlying: Gamma = d/dUnderlying Delta All options have positive gamma. Thus, every long option has delta exposure. Gamma is dynamic: Gamma increases with implied vol (ATM) Gamma increases as time to expiry decreases (ATM) Akuna Options 101 20  Gamma Scalping: If you are long gamma, you gain deltas in the direction the underlying moves. Thus, if you are constantly delta hedging, you are also scalping the underlying future since: As the underlying increases, you gain delta exposure and must sell more underlying As the underlying decreases, you lose delta exposure and must buy more underlying. You are thus, naturally buying low and selling high. Why not be always be long gamma then? Options cost some price. The price of that option and the delta of that option decays each day. This is called theta Eternal Struggle: Gamma vs. Theta A long gamma portfolio will, all other factors held constant, profit when the P&L from underlying movement exceeds the amount of theta paid. Similarly, a short gamma portfolio will, all other factors held constant, profit when the theta collected exceeds the amount lost due to movement in the underlying. Akuna Options 101 21  Note gamma scalping is inherently a bet about volatility. 💡 Definition: 1% Cash Gamma (Cash Gamma) is the amount by which our (cash) delta changes if the underlying changes by 1%. Cash delta and cash gamma are related by: Cash Gamma Delta per 1% = ​ Cash Delta Note that the Cash delta in the above equation is the cash delta of 1 future (since we’re only looking at deltas per 1% change in the future). Therefore, since the delta of a future is always 1, for cash gamma calculations we’d use cash delta as: Cash Delta = Future Price ⋅ multiplier. Example: 1. Crude oil future is currently $50 per barrel (one future has a cash delta of $50*1000 (1000 barrels per future) = $50,000. If we know we pick up 3 deltas for a 1% move, then our cash gamma per 1% is simply 3*50k = $150,000 Similarly, our trading screen can show us that we are long 150,000 cash gamma per 1%, and we can back out that we pick up the 3 deltas each 1% move. 2. In Cattle, the price of 1 future is 150 cents/pound and 1 contract equals 40,000 pounds of live cattle. If for every 1% move in the underlying our delta changes by 3 deltas, our cash gamma is simply $1.50 * 40,000 * 3= $180,000 Akuna Options 101 22  3.3: Theta 💡 Definition: The theta of an option is how much value that option loses daily. We call this loss theta decay. Theta is the same for a call and put on the same strike. Else, we violate PCP. Theta increases as we get clower to expiry for ATM strikes and is greatest near ATM strikes. Akuna Options 101 23  Theta is usually expressed as the amount “paid” or “received” each 24-hour period. I.e., a theta of +2,000 means we are short options and getting paid 2,000 every day in the loss in option value and a theta of -2,000 means we are long options and losing 2,000 every day. Example If we're long 100 options with a price of $2.00. In 24-hours the model will price them as $1.93. Therefore, the model will show that this option has a theta of 0.07. Since we're long 100 of them, and they have a multiplier of 100 our theta would be -0.07*100*100 = ($700) Central Tradeoff: Gamma vs. Theta The decision to hold an option is centrally a decision about whether to be long gamma or long theta and analyzing which one will out weight the other. One way to relate theta to gamma is to estimate the fair theta given gamma and vol: 2 Akuna Options 101 24  2 Cash Gamma ⋅ (std. dev. % move) "Fair Theta" = ​ 200 Example: If we have a cash gamma of 1,000,000 on a 16 vol (1% expected s.d. move per day), we get 1,000,000/200 = $5,000 theta as the fair theta for this position. If we our position is actually -8,000 theta, i.e. we are paying $8,000 a day in theta, then our position is called “inefficient”. 3.4: Volatility 💡 Definition: Volatility (vol), usually denoted as σ , is the annualized standard deviation of log returns Generally, the volatility for a time horizon, t, in years is expressed as σt = σannual ​ ​ t ​ Thus, given 252 trading days in a year, we have that t Expected 1 s.d. move over t days = σannual ​ ​ ​ ≈ σannual t/16 ​ 252 Volatility moves and price moves compound over time and so the right hand tail is fat on the vol distribution. Furthermore, vol and price are both lower bounded by 0. Thus, a lognormal distribution is typically used to model vol and price distributions: Akuna Options 101 25  Types of Vol: Historical/Realized Vol: Annualized standard deviation of close-to-close prices for each day over some fixed, historic time-frame. Historical Implied Vol: Implied vol observed from historic option prices over some fixed time-frame. Implied Vol: Expected/predicted future vol of the underlying asset. Implied vol is typically the input into an options pricing model. Thus, one may control options theos by changing implied vol in their model. Forward Vol: Expected average vol between the expiration dates of two options with successive maturities. Vol as a Measure of Movement: Vol numbers used in options pricing are a measure of the standard deviations of a product’s future price move. Akuna Options 101 26  Example: A 20% volatility would tell us that the underlying will be within 20% of the current underlying price with a 68% probability (1 standard deviation) a year from now. So, an underlying that is currently priced at $100 would be between $80 and $120 one year from today with a 68.3% probability. Similarly, it would be between $60 and $140 with a probability of 95% since that is 2 standard deviations from the current price. Thus, vol represents an expected price distribution of the underlying: Akuna Options 101 27  Historical Vol Calculation Example: There are a few things to note before calculating historical volatilities that differ from the usual calculation of standard deviations. Assuming we are calculating volatility from daily closing prices, we: Calculate log returns, not absolute returns Assume the mean of the returns is always zero. So, the formula of n-day annualized volatility looks like (using 252 trading days in a year): n 2 252 Sj ​ σhistoric = ​ ​ ∑ (log ​ ​ ) ​ n Sj −1 ​ j =0 where Si is the closing price on the i-th day. Here, the above formula estimates ​ historic vol by computing the sample daily variance, assuming returns are centered at 0, and scaling up to get an annualized vol number. Akuna Options 101 28  Note: Time-Variance is not additive: If we know the (annualized) vol over a 10- day period and the (annualized) vol over the next 10 days, the 20-day vol is NOT the average. Rather it is the square root of the average of the squares. 3.5: Vega 💡 Definition: The vega of an option is the first partial derivative of price wrt to implied vol. That is, vega is the option value price change per 1- point change in implied vol. By PCP, vega of a call and put on the same strike is the same. Vega is the most important greek for an OMM. Options traders are vega traders. Vega is dynamic: 1. Time to expiry a. Vega should increase with time to expiry since, over long time periods, increased implied vol is more likely to take an OTM option into the money. 2. Distance of Option from ATM a. Vega should decrease as the options moves further away from ATM. This is because the vol is far less likely to change the state of the option and the value is entirely determined by either the intrinsic or the extrinisc value. 3. Implied vol of the option a. TBD Akuna Options 101 29  Outright options always have positive vega. Below is the option vega surface across strikes and expires: Akuna Options 101 30  Example: Suppose an option has 0.081 vega. Then, buying 1000 of these options at a 50 multiplier gives us a total portfolio vega of 1000 * 50 * 0.081 = 4050. Calculating the vega of a portfolio of options = (number of options) x (multiplier) x (option vega) 3.6: Rho & Boxes 💡 Definition: Rho is the sensitivity of an option’s price to a change in interest rates (risk-free rate). Calls and puts on the same strike have different rho values. Akuna Options 101 31  Rho is typically expressed as a change in option price for a 1 point (1%) change in interest rates. Interest Rates: Interest rates change through time and we can model the curve in different ways to change our option prices. Boxes: As in the above curve, it is clear that one can express an opinion on how interest rates will change through options. Thus, we consider the boxes trade. Akuna Options 101 32 Akuna Options 101 33