What is the gamma of a European call option with the following parameters? As a reminder, gamma is defined as the first derivative of delta with respect to the stock price, or alternatively as the second derivative of the option price with respect to the stock price. s0 = $40k = $40 r = 10%sigma = 20%T = 0.75 years In order to avoid precision issues with Excel, please use an epsilon of 0.0001. (required precision 0.0001 +/- 0.0002)   Greeks Reference Guide: Delta = ∂π/∂S Theta = ∂π/∂t Gamma = (∂2π)/(∂S2) Vega = ∂π/∂σ Rho = ∂π/∂r

1. Consider a one period binomial model. Suppose So = 1 att = To; and Su = 2 and Sd = ½ at time T₁. If we assume the risk free rate R is 1.2, compute the current value of a European put with strike K = 1. Please round your answer to 2 decimals. Enter answer here 2. Compute the number of units of stock we need to short in order to replicate the option in the previous question. Please round your answer to 2 decimals. Enter answer here 3. Use Black-Scholes Formula to calculate the call price of a European call option with: So = 20, K = 20, r = 5%, c = 0,0 = 40%, T = 5; (round to two decimal digits).

Data: S0 = 120; X = 126; 1+r = 1.05. The two possibilities for ST are 150 and 102. (Round to 2 decimal places).  The range of S is 48 while that of C is 24 across the two states. What is the hedge ratio of the call? Hedge ratio ? Calculate the value of a call option on the stock with an exercise price of 126. (Do not use continuous compounding to calculate the present value of X in this example because we are using a two-state model here; the assumed 5% interest rate is an effective rate per period.) Call value ?

1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.7739. and put option value is 1.8101 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?

1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.77. and put option value is 1.99 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. explainc. What would be the extent of your profit in (a) depend on? explain

What is the implied volatility of a European call option with the following parameters? c = $3 s0 = $40 k = 41 r = 10% T = 0.5 years (Enter 11.51% as 0.1151. Required precision +/- 0.0002)

Suppose the nominal rate of return is 0.085 and the risk-free rate is 0.010. What is the risk premium? Instruction: Round to two decimal places. E.g., if your answer is 0.0106465 or 1.06465%, you should type ONLY the number .01, neither 0.0106465, 0.0106, nor 1.065. Otherwise, Blackboard will treat it as a wrong answer.

Use the Black-Scholes model to value a call option with the following data: Price $34 Exercise price 30 Risk-free rate 0.04 time to expiry 0.5 0.31557 0.099584 0.762113 0.538972 0.777004 0.705047 Post your answer with 2 decimal places 5 0² d1= d2= Nd1= Nd2=

The following information is given about an Option on a stock: S(0)=$31, X=$34, rf=9%, variance (sigma squared)=20%, T=182.5 days, Dividend $1.75 in 45 days (1) Calculate the price of a European put option using the Black-Scholes pricing model (show all workings including d1, d2, N(d1), N(d2)) (2) Calculate the price of the corresponding European call option (hint: put call parity) (3) Suppose you feel that the put option is overpriced. What strategy should you use to exploit the apparent mispricing? (4) The market has entered a state of significant volatility, and you believe the implied volatility is incorrect. You believe it should be 10% higher. What trade would you undertake to exploit this arbitrage

Write down the formula for: fa) price of an European put option f6) price of a European calli option Koth on a non-dividend paying stock and Koth derived from the Black-Scholes-Merton Differential Equations Define every symbol in the formulae. Given that, with the usual notation, S, = 42, K = 40, r3D0.1, о %3D0.2, Т%3D0.5 N(0.7693) N(0.6298) = 0.7340 0.7791 4.79 Calculate the price of a European call option on the stock. Consider an option on a dividend paying stock with the following characteristics s, = $30 Going ex-dividend in 1.5 months. Expected Dividend is $0.5 Exercise Price is $29. Risk free rate is 5% per annum Volatility is 25% per annum Time to maturity is 4 months Calculate price if (a) European Call (b) European Put 2.52 2.52 Given further N (.3068) = 0.6205 N (.1625) = 0.5645