Chp5-Colour PDF - Financial Markets & Intermediaries

Boğaziçi University – Department of Economics Financial Markets and Intermediaries L.Yıldıran (2024-2025) Chapter 5 – DERIVATIVE ASSETS (Forwards, Futures, Options, Swaps) A derivative asset derives its value from another as...

Boğaziçi University – Department of Economics Financial Markets and Intermediaries L.Yıldıran (2024-2025) Chapter 5 – DERIVATIVE ASSETS (Forwards, Futures, Options, Swaps) A derivative asset derives its value from another asset (the underlying asset), e.g., commodity, stock, bond, FX, etc. While other financial assets (stocks, bonds, bills, commercial papers, preferred stocks, convertibles, etc.) are to raise new capital, derivative assets are to manage risks. Risk-averse people use three methods to manage (eliminate/reduce) risks: Insurance, Diversification, and Hedging. Long Position: If you have an asset or if you will receive an asset, then you have a long position of that asset. Short Position: If you sell an asset or if you will give/deliver an asset, then you have a short position of that asset. Hedging: Protection against risk by taking a counter position to your original position. Originally long ® create a short position; originally short ® create a long position Hedging is a special case of diversification. The original asset is diversified with another asset, which is perfectly negatively correlated with the original asset. Derivative assets are used o To hedge risks § Interest rate risk: Forward/Future/Option/Swap Contracts § FX rate risk: Forward/Future/Option/Swap Contracts § Credit risk: Credit Default Swap (CDS) o For speculation (not to be confused with manipulation): To bet on future prices (without an original position) ® gambling Forward Contracts Originally on commodities, e.g., cotton, rice, wheat, oil, etc. Example: "! = $0.7/kg or $1/kg or $1.3/kg P0 (spot price) = $1/kg for cotton, 𝑃 Farmer is afraid that future prices will fall. Merchant is afraid that future prices will rise. Farmer has a long position of cotton initially. He has to create a short position to be able to hedge the price risk. To do so, he sells a forward contract (i.e., he promises to sell cotton at predetermined conditions). The merchant, with the opposite concern, buys a forward contract (i.e., he promises to buy cotton at predetermined conditions. Forward contract specifies: ® Commodity (cotton of a certain grade/quality) ® commodity has to be a standard product ® Quantity (1 ton) ® Delivery time, (T = 6 months) ® Future (contract) price (Pf = $1/kg) Now ® no exchange/no money/no cotton ® only the contract Ex-ante, both are better off, neither needs to worry about future prices 1  At the delivery date ® 1 ton of cotton is exchanged with $1000 Ex-post, ® If PT (actual price) > Pf Þ farmer loses & merchant gains from the forward deal ® If PT (actual price) < Pf Þ farmer gains & merchant loses from the forward deal Notice: At T-1, if PT-1 = $1.2/kg Þ PForward Contract ≈ $200 Pay-offs from the forward contract (zero-sum game) Pay-offs to farmer Merchant Cotton (Long P.) 1 P1 P1 1 Farmer Forward Contract (Short P.) Financial Forward Contracts Example: Hedging (against) interest rate risk You have a government coupon bond (long position) Face value= $1000, maturity= 10 years, c=10%, k=10%, P0=$1000 You need to liquidate it next year, but Afraid that next year k­, P1¯ Þ interest rate risk. How to hedge interest rate risk? Create a short position; sell a forward contract (i.e., promise to sell/deliver that bond at Pf = $1000) Buyer expects to have $1000 next year. He wants to obtain 10% return, but is afraid that next year k¯, P1­. So, to fix the future return/price He buys a forward contract (i.e., promises to buy that bond at Pf = $1000) At delivery date: k=12% Þ P1 < Pf Þ you gain, buyer loses k=8% Þ P1 > Pf Þ you lose, buyer gains Problems with Forward Contracts: o Liquidity: Difficult to find a counter party with the exact match/concern o Default Risk: Ex-post, the counter party may default or bankrupt ® litigation is costly Future Contracts An institution is involved (contract is made with the institution, not directly with the counter party): This institution can be: A clearinghouse in an organized exchange (Chicago Board of Trade, İzmir VOB ® BİST) or A bank or another financial institution in OTC markets 2  Liquidity is improved by standardizing the underlying asset (E.g., if we continue from the previous example: all government bonds with T ³ 5 years, 12 different days in a year as delivery time). As long as the institution is financially sound, no default risk for the buyer or seller. Institution: to reduce the counterparty default risk, it imposes Þ Margin Requirement: Both seller and buyer have to deposit a certain amount (e.g., 2% of the notional/contractual amount) as collateral (to be used in case of default), in their accounts at the institution. Margin Call: Balances at these deposit accounts are adjusted daily (marked to market) depending on price changes. The losing party is called for to meet the margin requirement. Example: Continue from the previous example (Financial Forward Contract) Margin requirement, $20 (= %2x1000) ® Leverage = 1000/20 = 50 For simplicity, let’s ignore the service fee of the institution Days after contract Price ($) Seller Buyer 0 1000 20 20 1st day 1001 19+1 21 2nd day 1002 19+1 22........ 200th day (delivery) 1200 20 220 On the delivery day: i. Physical Exchange: Bond « $1000. Since commitments are fulfilled, each party gets all he/she has already deposited (Seller=220, buyer=20). ii. No Physical Exchange: Seller does not show up. Buyer walks away with the money he/she gets from the intermediary (220). Buyer can then buy the bond at the market place at $1200. Pay-offs from the future contract: Pay-offs to seller Buyer Bond (Long P.) P1 800 1000 1200 P1 800 1000 1200 Seller Future Contract (Short P.) Example: Using derivative assets for speculation You have no initial position of $. Now P0= 34 TL/$, but you expect that ® PT = 38 TL/$ Þ take a long position, buy a forward contract at Pf < 38 TL/$ (e.g., Pf =36) ® PT = 30 TL/$ Þ take a short position, sell a forward contract at Pf >30 TL/$ (e.g., Pf =32) (you short-sell $) Notice: If your expectations come true, you earn 2 TL/$ with no initial position and investment. 3  Option Contracts Call Option: The right to buy something (i.e., the underlying asset) at a predetermined price (exercise price); You buy a call option if you expect/worry that the future price of the underlying asset will rise. Put Option: The right to sell something (i.e., the underlying asset) at a predetermined price (exercise price); You buy a put option if you expect/worry that the future price of the underlying asset will fall. Notice: With Forward/Future Contracts you commit/promise to buy/sell the underlying asset at a predetermined price. With Option Contracts you buy the right to buy/sell the underlying asset at a predetermined price. Exercising that right is (optional) up to you. Example: Stock call option S0, S1, c, X, T S0 = $100, T = 1 month, X = $105, c = $3 Pay-offs (∆ W) Call Option S1 105 108 -3 Pay-offs Pay-offs Buyer/owner of put Buyer/owner of call c p X X -p -c Seller/writer of call Seller/writer of put 4  Option Pricing: 𝑐/𝑝 = 𝑓(𝑆! , 𝑋, 𝑇, 𝜎 " , 𝑟# ) Black-Scholes-Merton Formula: 𝑐 = 𝑆" 𝑁(𝑑# ) − 𝑋𝑒 $%! ! 𝑁(𝑑& ) 𝑝 = 𝑋𝑒 $%! ! 𝑁(−𝑑& ) − 𝑆" 𝑁(−𝑑# ) 𝑆 𝜎2 𝑙𝑛 𝑋" + 6𝑟' + 2 8 𝑇 𝑤ℎ𝑒𝑟𝑒, 𝑑# = , 𝑑& = 𝑑# − 𝜎√𝑇 , 𝑁 = 𝑁𝑜𝑟𝑚𝑎𝑙 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝜎√𝑇 𝜕𝑐 𝜕𝑐 𝜕𝑐 𝜕𝑐 𝜕𝑐 𝜕𝑝 𝜕𝑝 𝜕𝑝 𝜕𝑝 𝜕𝑝.𝜕𝑆 > 0, 𝜕𝑋 < 0, 𝜕𝑇 > 0, > 0, 𝜕𝑟# > 0 4 𝜕𝑆 < 0, 𝜕𝑋 > 0, 𝜕𝑇 > 𝑜𝑟 ≤ 0 , > 0, 𝜕𝑟# < 07 ! 𝜕𝜎 " ! 𝜕𝜎 " Put-Call Parity: For put and call options on the same underlying asset and with the same characteristics ® c > p American vs. European Options: American Option owner can exercise his/her right at any time before the expiration date. European Option owner can exercise his/her right only at the expiration date. Forming a Riskless Portfolio: You buy a Stock S You sell a Call Option on S with Xc = S0 You buy a Put Option on S with Xp = S0 Now, notice that S-C+P = Bond Pay-offs Pay-offs S S S+P s S+P-C X P X P -C -C 5  Straddle: 1 put + 1 call on S, with X=S0 Loss for small changes in S, gain for large changes in S Hedging (against) FX Rate Risk: Example: Importer will pay in 2 months $1mil ® 34 mil TL Afraid that FX rate will­ (depreciation of TL), Currently he has short position of dollar. To hedge, he should take a long position ® Buy a forward/future F=34 TL/$ ® Buy a call option X=34 TL/$ (c=0.2 TL/$) Pay-offs Forward - Future Call Option -0.2 Short Position 34 6