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The price of one-year and two-year European put option with strike price $100 are $10 and $4 respectively. The term-structure of interest rate is 10%. Is there any arbitrage opportunity? If yes, perform the arbitrage.
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- 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. 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-Scholes-Merton model, compute the price of a put 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.A. Using the Black model, calculate the price of a call option on a forward contract.B. Calculate the underlying asset's price. Using the Black-Scholes-Merton model, determine the price of a call option on the underlying asset. Should this pricing be any different from the one calculated in letter A? Explain your answer.C. Using the Black model, calculate the price of a put option on a forward contract.D. Using the Black-Scholes-Merton model, compute the price of a put option on the underlying asset. Should this pricing be any different from the one calculated in letter C? Explain your answer.
- 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. A. Using the Black model, calculate the price of a call option on a forward contract. B. Calculate the underlying asset's price. Using the Black-Scholes-Merton model, determine the price of a call option on the underlying asset. Should this pricing be any different from the one calculated in letter A? Explain your answer. C. Using the Black model, calculate the price of a put option on a forward contract. D. Using the Black-Scholes-Merton model, compute the price of a put option on the underlying asset. Should this pricing be any different from the one calculated in letter C? Explain your answer.Suppose a European call option on a sack of corn with a strike price of $50 and a maturity of one-month, trades for $5. What is the price of the put premium with identical strike price and time until expiration, if the one-month risk-free rate is 2% and the spot price of the underlying asset is $53?A European call that will expire in one year is currently trading for $3. Assume the risk-free rate (based on continuous compounding) is 5%, the underlying stock price is $60 and the strike price is $55. a. Is there an arbitrage opportunity? b. Describe exactly what a trader should do to take advantage of the arbitrage opportunity assuming it exists. c. Determine the present value of the profit that the trader can earn assuming you identify an arbitrage opportunity. Use at least four decimal places for those questions that require a numerical answer.
- 1. 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.Suppose that at the present time, one can enter 5-year swaps that exchange SOFR for 4%. An off-market swap would then be defined as a swap of SOFR for a fixed rate other than 4%. For example, a firm with 8% coupon debt outstanding might like to convert to synthetic floating- rate debt by entering a swap in which it pays SOFR and receives a fixed rate of 8%. What up- front payment will be required to induce a counterparty to take the other side of this swap? Assume notional principal is $110 million. Note: Do not round intermediate calculations. Round your final answer to the nearest dollar amount. X Answer is complete but not entirely correct. Up-front payment 2,174,000 X $A European call and put option on the same security both expire in threemonths, both have a strike price of $20 and both sell for a price of $3. If the nominalcontinuously compounded interest rate is 10% and the stock price is currently $25,identify an arbitrage.
- A put option with an exercise price of $65 will expire in 180 days. The underlying asset price of today is $173. The underlying asset price at expiration is $166. The risk-free rate is 2%, What is the lower bounds for an European put?Suppose the European call and put options with strike price $20 and maturity date in 1 month cost $2.0 and $1.0, respectively. The underlying stock price is $18 and the risk-free continuously compounded interest rate is 8%. (a) Is there an arbitrage opportunity? (b)If yes, how would you implement arbitrage opportunity?Suppose that at the present time, one can enter 5-year swaps that exchange LIBOR for 5%. An off-market swap would then be defined as a swap of LIBOR for a fixed rate other than 5%. For example, a firm with 11% coupon debt outstanding might like to convert to synthetic floating-rate debt by entering a swap in which it pays LIBOR and receives a fixed rate of 11%. What up-front payment will be required to induce a counterparty to take the other side of this swap? Assume notional principal is $95 million. (Do not round intermediate calculations. Round your final answer to the nearest dollar amount.)