Introduction to Derivatives and Instruments

Underlying Instruments

• Financial instruments include bonds, stocks, currencies, indexes, and other derivatives.
• Non-financial instruments encompass commodities like metals, grains, livestock, electricity, gas, and oil, as well as weather derivatives.

Derivatives

• A derivative derives its value from another financial instrument's price and involves a contract between two parties, with terms set today and delivery at a future date.
• Main types of derivatives: options, forwards/futures, swaps.

Options

• An option is a contract giving the buyer the right, but not the obligation, to buy or sell an underlying asset at a specified price before or at expiration.
• American Options can be exercised any time up to expiration, while European Options can only be exercised at expiration.

Forwards and Futures

• Forwards and futures are contracts obligating two parties to exchange assets at a future date for a specific price.

Swaps

• Swaps involve two parties exchanging future cash flows from different financial instruments, essentially a chain of futures.

Market Types

• Spot Market: Immediate delivery of financial instruments.
• Exchange Listed Markets: Regulated markets with defined position and order limits.
• Over-the-Counter Markets: Customized contracts without restrictions.

Arbitrage

• Arbitrage involves profiting from price discrepancies of the same asset in different markets.
• The Law of One Price indicates price equality for the same asset in different markets.

Market Positions

• Long Position (Taker): Buyer of the option; expects the stock price to rise.
• Short Position (Writer): Seller of the option; expects the stock price to stay below the strike price.

Call and Put Options

• Call Options: Right to buy the underlying asset.
• Put Options: Right to sell the underlying asset.
• Positions can be long (buy) or short (sell), depending on expectations of price movements.

Intrinsic Value

• For Call Options: Intrinsic value is the difference between the spot and exercise prices (max(0, Spot Price - Strike Price)).
• For Put Options: Intrinsic value is the difference between the exercise and spot prices (max(0, Strike Price - Spot Price)).

Open Interest & Put/Call Ratio

• Open Interest: Number of outstanding option contracts; higher indicates more interest in particular options.
• Put/Call Ratio (PCR): Indicates market sentiment; high PCR (>1) suggests bearishness, while low PCR indicates bullishness.

Time Value

• Time Value represents the potential for future price increases; premium of an option comprises intrinsic and time value.
• Longer time until expiration typically results in higher premium due to increased uncertainty.

Option Boundaries

• Call Options have a minimum value of max(0, Spot Price - Exercise Price) for American Options.
• Put Options have a minimum value of max(0, Exercise Price - Spot Price) for American Options.

Pricing Factors

• Call Options premiums depend on exercise price, current spot price, volatility, time to expiration, and interest rates.
• Put Options premiums similarly depend on these factors but inversely correlate with exercise prices.

Dividends and Early Exercise

• Dividends impact option values; call options may be exercised early before a dividend payment to capture value.
• American Options allow early exercise, primarily benefiting from the timing of dividend announcements.

Summary of Call and Put Options

• Call Options:
  • In the money (ITM) when spot price exceeds strike price.
  • Out of money (OTM) when spot price is below strike price.
• Put Options:
  • ITM when spot price is below strike price.
  • OTM when spot price is above strike price.

Example Evaluation

• Call and put options have varying premiums based on their exercise prices; lower exercise prices for calls and higher for puts lead to increased premiums due to better profitability prospects.### Time Value and Options
• Time value affects option pricing: longer expiration yields higher value, while shorter expiration leads to lower value.
• American Puts are generally worth more than European Puts due to early exercise options.
• American Calls are equally or more valuable than European Calls, as they too allow early exercise.
• Early exercise of American Puts becomes less likely when stock dividends are high, as exercising forfeits future dividends.

Interest Rates and Options

• Call options provide financial leverage: less initial investment compared to buying the stock outright allows funds to be allocated to interest-earning investments.
• Delaying the sale of a stock through a put option means potential lost interest earnings from immediate sales due to high interest rates.
• Higher market interest rates diminish the value of put options as they incentivize immediate selling and investing in higher rates.

Volatility's Impact on Options

• Increased volatility enhances the value of Call options, offering the potential for higher profits when the market rises.
• Conversely, higher volatility also increases Put options' value as it limits losses to the premium paid, while allowing for gains from price drops.

Put-Call Parity

• Put-Call Parity is a key principle to determine price relationships between puts and calls.
• Two portfolios analyzed: Portfolio A (European Put + Stock) and Portfolio B (European Call + Bond).
• Pay-offs for both portfolios equalize under various market conditions, confirming the relationship that PV(Stock) + Put = Call + PV(Bond).

European Options Pricing

• The pricing relationship for European options:
  • Value of a European Put = Call Option + Bond - Stock
  • Value of a Call Option = Stock + Put Option - Bond

American Options Considerations

• American options can incorporate present value adjustments for dividends, affecting their pricing dynamics.

Example Analysis: ANZ Options

• Call option for ANZ has a cost of $0.52, spot price of $15.74, and exercise price of $16.00.
• Put option for ANZ costs $0.60, also with a spot price of $15.74 and exercise price of $16.00.
• The Put costs more than the Call because it is "in the money" while the Call is "out of the money".
• Example confirms that Put-Call Parity holds since the values align when calculated.

Illustrating Call and Put Value Comparison

• An "At the money call option" should be priced higher than an "At the money put" due to risk-free returns.
• Rearranging pricing formulas shows: as spot price equals exercise price (S = X), Call Price will always equal Put Price plus the risk-free rate.