Option Pricing and Applications: Currency Risk and Convertible Bonds
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Presentation Transcript
Today • Options • Option pricing • Applications: Currency risk and convertible bonds • Reading • • Brealey, Myers, and Allen: Chapter 20, 21
Options • Gives the holder the right to either buy (call option) or sell (put option) at a specified price. • Exercise, or strike, price • Expiration or maturity date • American vs. European option • In-the-money, at-the-money, or out-of-the-money
Valuation • Option pricing • How risky is an option? How can we estimate the expected cashflows, and what is the appropriate discount rate? • Two formulas • Put-call parity • Black-Scholes formula * • * Fischer Black and Myron Scholes
Option Values • Intrinsic value - profit that could be made if the option was immediately exercised (內在價值、真實價值) • Call: stock price - exercise price • Put: exercise price - stock price • Time value - the difference between the option price and the intrinsic value
Time Value of Options: Call Option value Value of Call Intrinsic Value Time value X Stock Price
Factors Influencing Option Values Factor Stock price Exercise price Volatility of stock price Time to expiration Interest rate Dividend Rate
Put-call parity • Relation between put and call prices • P + S = C + PV(X) • S = stock price • P = put price • C = call price • X = strike price • PV(X) = present value of $X = X / (1+r)t • r = riskfree rate
Put-Call Parity Relationship Long a call and write a put simultaneously. Call and put are with the same exercise price and maturity date.
Put-Call Parity Relationship ST< X ST > X Payoff for Call Owned 0 ST - X Payoff for Put Written -( X -ST) 0 Total Payoff ST - XST – X PV of (ST-X)= S0 - X / (1 + rf)T
Payoff of Long Call & Short Put Payoff Long Call Combined = Leveraged Equity Stock Price Short Put
Arbitrage & Put Call Parity Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal. C - P = S0 - X / (1 + rf)T If the prices are not equal, arbitrage will be possible
Put Call Parity - Disequilibrium Example Stock Price = 110, Call Price = 17, Put Price = 5 Risk Free = 5% per 6 month (10.25% effective annual yield) Maturity = .5 yr X = 105 C - P > S0 - X / (1 + rf)T 17- 5 > 110 - (105/1.05) 12 > 10 Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative
Put-Call Parity Arbitrage ImmediateCashflow in Six Months Position Cashflow ST<105 ST> 105 Buy Stock -110 ST ST Borrow 100 X/(1+r)T = 100 +100 -105 -105 Sell Call +17 0 -(ST-105) Buy Put -5 105-ST 0 Total 2 0 0
Using Black-Scholes • Applications • Hedging currency risk • Pricing convertible debt
Currency risk • Your company, headquartered in the U.S., supplies auto parts to Jaguar PLC in Britain. You have just signed a contract worth ₤18.2 million to deliver parts next year. Payment is certain and occurs at the end of the year. • The $ / ₤ exchange rate is currently S$/₤ = 1.4794. • How do fluctuations in exchange rates affect $ revenues? How can you hedge this risk?
Convertible bonds • Your firm is thinking about issuing 10-year convertible bonds. In the past, the firm has issued straight (non-convertible) debt, which currently has a yield of 8.2%. • The new bonds have a face value of $1,000 and will be convertible into 20 shares of stocks. How much are the bonds worth if they pay the same interest rate as straight debt? • Today’s stock price is $32. The firm does not pay dividends, and you estimate that the standard deviation of returns is 35% annually. Long-term interest rates are 6%.
Convertible bonds • Call option • X = $50, S = $32, σ = 35%, r = 6%, T = 10 • Black-Scholes value = $10.31 • Convertible bond
