Exercise 5.2 Suppose you pay 5 to buy a European (K = 100, t = 1/2) put option on a given security. Assuming a nominal annual in- terest rate of 6 percent, compounded monthly, find the present value of your return from this investment if (a) S(1/2) = 102; (b) S(1/2) = 98.
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- Find the hedge ratio a 1-period at-the-money put option on ¥300,000. The spot exchange rate is ¥100 = $1.00. In the next period, the yen can increase in dollar value by 15 percent or decrease by 10 percent. The risk-free rate in dollars is i$ = 5%; The risk-free rate in yen is i¥ = 1%. A.-0.44 B.-0.66 C.-0.60 D.-0.401. Suppose that, in each period, the cost of a security either goes up by a factor of u = 2 or down by a factor d = 1/2. Assume the initial price of the security is $100 and that the interest rate r is 0. c) Assuming the strike price of a European call option on this security is $90, compute the possible payoffs of the call option given that the option expires in two periods.D3 show the solution in details Use the binomial option pricing model to find the value of a call option on £10,000 with a strike price of €12,500. The current exchange rate is €1.50/£1.00 and in the next period the exchange rate can increase to €2.40/£ or decrease to €0.9375/€1.00 (i.e. u = 1.6 and d = 1/u = 0.625). The current interest rates are i€ = 3% and are i£ = 4%. Choose the answer closest to yours. the answer is A) €3,275
- Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. Using the Black-Scholes-Merton model, compute the price of a put option on the underlying asset.Q1 Consider the option on currency HKD against the USD: • Current spot rate is HKD7.50 for 1 USD • Risk-free HKD rate of interest is 5% p.a. • Risk-free USD rate of interest is 2% p.a. • Volatility (σ) of the currency returns is 20% p.a. • Maturity of the option is 3 months. • Strike rate of the option is HKD8.00 for 1 USD • The currency options are European in nature Answer the following questions. (i) How much does it cost to hold (i.e., buy) a call-HKD option? Use the Garman Kohlhagen model.Q1 Consider the option on currency HKD against the USD: • Current spot rate is HKD7.50 for 1 USD • Risk-free HKD rate of interest is 5% p.a. • Risk-free USD rate of interest is 2% p.a. • Volatility (σ) of the currency returns is 20% p.a. • Maturity of the option is 3 months. • Strike rate of the option is HKD8.00 for 1 USD • The currency options are European in nature Answer the following questions. (i) How much does it cost to hold (i.e., buy) a call-HKD option? Use the Garman Kohlhagen model. (ii) What is the minimum terminal exchange rate for the holder of the call-HKD option to profit from holding the currency option? (iii) How much does it cost to hold (i.e., buy) a put-HKD option? Do not use the Garman Kohlhagen model.
- Consider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45. a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage? b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.Suppose you pay 10 to buy a European (K = 100, t = 2) call option on a given security. Assuming a continuously compounded nominal annual interest rate of 6 percent, find the present value of your return from this investment if the price of the security at time 2 is (a) 110; (b) 98.Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. Using the Black model, calculate the price of a put option on a forward contract.
- Determine the risk-neutral value for a European put option (for a FLB (First Local Bank) share) that expires in eight months. The strike price is R500 and the current price is R650. The interest rate is 11%, and the volatility of the security is 0.026. *DO NOT USE EXCEL OR ANY OTHER PLATFORM, SHOW STEP-BY-STEP CALCULATIONAssume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. Calculate the underlying asset's price. Using the Black-Scholes-Merton model, determine the price of a call option on the underlying asset.Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. Using the Black model, calculate the price of a call option on a forward contract.