Consider a model for a security with time zero value S0 = 150, a yearly effective interest rate of .01% and volatility σ^2 = (.02)^2 . Implement a binomial model to price option in python.
3. Price an Asian Call Option with payoff ((1/T)(Integral from 0 to T)(Stdt) − X)+ with expiry T = 1/2 years and strike price X = 150. Carry out the binomial model in N = 25 an N = 50, steps.
Consider a model for a security with time zero value S0 = 150, a yearly effective...
Consider the BS model with S0=120,μ=0.2,r=0.04,T=1 and σ=0.3. The price of a call option with strike price K=100 is
Use the following information to respond to problems S0= $40; σ= 40%; r = 0.03; D = $0; T = 1. Find the value of an American call option with a strike price of $45 using a two-step binomial model
In a binomial tree model, S0=33. In the next period, ST is either 35 or 30. Assume interest rate is 0. Calculate the price of a call option with strike equal to 31. 1 1.6 2 2.4
1. (Put-call parity) A stock currently costs So per share. In each time period, the value of the stock will either increase or decrease by u and d respectively, and the risk-free interest rate is r. Let Sn be the price of the stock at t-n, for O < n < N, and consider three derivatives which expire at t - V, a cal option Voll-(SN-K)+, a put option VNut-(X-Sy)+, and a forward option VN(SN contract FN SN N) ,...
I. Consider the N-step binomial asset pricing model with 0 < d < 1 + r < u. Assume N = 3, So 100, r = 0.05, u = 1.10, and d 0.90. Calculate the price at time zero of each of the following options using backward induction (a) A European put option expiring at time N 2 with strike price K-100 (b) A European put option expiring at time N 3 with strike price K- 100 (c) A European...
In a binomial tree model, S0=32. In the next period, ST is either 35 or 30. Assume interest rate is 0. Calculate the price of a call option with strike equal to 31. A. 0.6 B. 1 C. 1.6 D. 2
1. (Put-call parity) A stock currently costs So per share. In each time period, the value of the stock will either increase or decrease by u and d respectively, and the risk-free interest rate is r. Let Sn be the price of the stock at t n, for O < n < V, and consider three derivatives which expire at t- N, a call option Vall-(SN-K)+, a put option Vpul-(K-Sy)+, ad a forward contract Fv -SN -K (a) The forward...
5. Consider the 3-period binomial model with So 100, u 2, dand r-1. (a) What is the current price of a lookback call option with a strike price of $100 that pays off (at time three) V3- max Sn - 100 Sn3 (b) What is the time-zero price of a lookback put option with a strike price of $100 that pays off (at time three) V 100-min Sn OSnK3 (c) What is the time-zero price of an Asian call option...
14. Note that the Black-Scholes formula gives the price of European call c given the time to expiration T, the strike price K, the stock’s spot price S0, the stock’s volatility σ, and the risk-free rate of return r : c = c(T, K, S0, σ, r). All the variables but one are “observable,” because an investor can quickly observe T, K, S0, r. The stock volatility, however, is not observable. Rather it relies on the choice of models the...
1) consider a CRR model T = 2, S0= $100 , S1 = $200 or S1 = $50 an associated European call option with strike price k = $80 and exercise time T = 2 assume that the risk free interest rate r = 0.1 a) draw the binary tree and compute the arbitrage free initial price of the European call option at time zero. b) Determine an explicit hedging strategy for this option c) Suppose that the option is...