We are given a single-period binomial model with A(0) = 10, A(T) = 20,S(0) = 100 and S(T) = 210 with probability 0.5 and S(T) = 90 with probability 0.5. Assuming no arbitrage exists, find the price C(0) of a call option with strike price X = 150.
We are given a single-period binomial model with A(0) = 10, A(T) = 20,S(0) = 100...
5. Consider the single period binomial model as in Section 1.2.2. Suppose that d <1+r <u. Show that if there exists an arbitrage opportunity (as in Definition 1.5), then one can find an arbitrage opportunity with V = 0. This means that there is no net cash flow at time 0. (Note: This is a step in the proof of Proposition 1.7 which you should go through carefully.) 1.2.2 Formal logical content The theory we build will be a mathematical...
Consider the following one-period binomial model for stock price. At t = 0 the stock price is $80 and at t = 1 (t is in years) it could be $70 with probability p > 0 and $y with probability 1 − p. The interest rate is assumed to be 8%. (1) Determine the range of values for y that precludes arbitrage in this model. (2) Assume that y = $83. Construct an arbitrage strategy for this model.1
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...
1. (5 points) Find the value of a call option using a one-period binomial lattice model. The underlying stock has initial price $100 and lattice parameters u = 5/4, d = 4/5. The risk free interest rate is 10% and the strike price is $105.
PROBLEM 2. Consider a two-step Binomial model. In Figure 1 you are given an incomplete pricing tree, which corresponds to a European put option with strike price K = 65. (a) (5 Points) Compute the per period interest rate r and the risk-neutral probability p*. (b) (10 Points) Find the price of the put option at t = 0. Moreover, determine the complete binomial tree for the stock price. 2.6545 PE(O) 14.6 17.09 35.06 Figure 1: European put with K...
2. Consider the N-step binomial asset pricing model with 0 < d<1< u (a) Assume N-3. Sİ,-100, r-0.05, u-1.10, and d-0.90. Calculate the price at time (b) If the observed market price of the option in part (a) is $25 give a specific arbitrage trading (c) Suppose you wish to earn a profit of $100,000 from implementing your arbitrage trading zero, VO, of the European call-option with strike price K = 87.00. strategy to take advantage of any potential mis-pricing....
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
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
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14. Consider a one period binomial model. The initial stock price is $30. Over the next 3 months, the stock price could either go up to $36 (u = 1.2) or go down to $24 (d = 0.8). The continuously compounded interest rate is 6% per annum. Use this information to answer the remaining questions in this assignment. Consider a call option whose strike price is $32. How many shares should be bought or...
Problem #1 Imagine that the price of a given stock at time t is given with + (1 - wHp - No100), where R = 1,w = 0.5, Hp = 100,000 = 1. i) Let D, = 200 and N, = 100. What is the price of the stock in this case? ii) Now imagine that an investor purchases a call option that allows her to acquire this stock at time t + 1 for K = 150. Will this...