Consider an option on a non-dividend-paying stock when the stock price is $28, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. Using the Black-Scholes-Merton approach, What is the price of the option if it is a European call? What is the price of the option if it is an American call? What is the price of the option if it is a European put? Show that put–call parity holds.

Consider the following data (interest rate is per period): S = 100; K = 75;R = 1.20 ; u = 1.5 ; d = .5. 1. What is the binomial price of a European call option with two periods until expiration? What is the price an American option with the same strike price and same time to expiration. Is there ever early exercise? 2. Show that the binomial option price for a European put option with two periods to go until expiration is 3.125. Show that the binomial price for an American put is 6.25. Can you conclude from the difference in prices alone that early exercise may be optimal? When is it optimal? 3. Use your answers to (i) and (ii) to verify that put-call parity holds for European options, but not for American options. Explain all answers in detail or step by step solution.

Suppose that a European call option to buy a share for $ 90.00 costs a . Under what circumstances will the SELLER of the option make a profit ? \$4.00 and is held until maturity . ( DRAW the GRAPH to show ALL answers ) b . when will the option be exercised ( at what price , show on graph ) ? c . What is the Maximum profit for SELLER and at what stock price ? d . What is the Maximum loss for SELLER and at what stock price ? e . What will be profit / loss for SELLER if St is 150 ?

Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset ... what is the value of the call option? Call Option Price = $4.84 Call Option Price = $2.95 Call Option Price = $7.93 Call Option Price = $12.04

Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset … what is the value of the call option?

Consider a European call option on a non-dividend-paying stock where the stock price is $33, the strike price is $36, the risk-free rate is 6% per annum, the volatility is 25% per annum and the time to maturity is 6 months. (a) Calculate u and d for a one-step binomial tree. (b) Value the option using a non arbitrage argument. (c) Assume that the option is a put instead of a call. Value the option using the risk neutral approach. (d) Verify that the European call and European put prices found in (b) and (c) satisfy the put-call parity.

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?

We are looking at a European put option and a European call option written on the same underlying asset, same exercise price and same time to expiration. There is no dividend paid prior to expiration. The current stock price is $130 and the exercise price is $125. Suppose you have figured out the delta of the put option is -0.4451, what is the delta of the call option? 0.4451 0.5549 -0.5549 -0.4451

Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months.   a) What is the price of the option if it is a European put?

1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.