emm
Consider the following discrete time one-period market model. The savings account is given by Bo1 and B1-r-1.1. The stock price is given by So-1 and Si ξ where ξ is a random variable taking two possible values u 1.2 and d 0.9. Consider a put option whose payoff at time 1 is P (1- Si). rice 1S given by (a) Find a replicating strategy for this option. By considering the value of the replicating strategy, find the time 0 price of the put option Po (b) Find the price Po using a second method via the Equivalent Martingale Measure (EMM)
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1. Consider the following discrete time one-period market model. The savings account is given by Bo 1 and B1 1.1. The stock price is given by So 1 and S,-ξ where ξ is a random variable taking two pos...
1. Consider the following discrete time one-period market model. The savings account is given by Bo 1 and B1 1.1. The stock price is given by So 1 and S,-ξ where ξ is a random variable taking two possible values u 1.2 and d = 0.9. Consider a put option whose payoff at time l is P = (1-S)+. (a) Find a replicating strategy for this option. By considering the value of the replicating strategy, find the time 0 price...
2. Let Bt denote a Brownian motion. Consider the Black-Scholes model for the price of stock St, 2 So-1 and the savings account is given by β,-ea (a) Solve the equation for the price of the stock St a...
2. Let Bt denote a Brownian motion. Consider the Black-Scholes model for the price of stock St, 2 So-1 and the savings account is given by β,-ea (a) Solve the equation for the price of the stock St and show that it is not a (b) Explain what is meant by an Equivalent Martingale Measure (EMM) martingale. State the Girsanov theorem. Give the expression for Bt under the EMM Q, hence derive the expression for St under the EMM, and...
The current price of the Gilead stock is $77 per share. Consider an option strategy, which...
The current price of the Gilead stock is $77 per share. Consider an option strategy, which consists of following positions: Selling one put option on the Gilead stock with the strike price of $75. The price of this put option is $3.44. Buying one put option on the Gilead stock with the strike price of $72. The price of this option is $2.24. Buying one call option on the Gilead stock with the strike price of $81. The price of...
please type your answer 4. Consider a portfolio consisting of 6 stocks and 10 put options...
please type your answer
4. Consider a portfolio consisting of 6 stocks and 10 put options on the stocks. The current stock price is So = 100 and the stike price of the options is X = 100. The stock price can take on only two values at maturity T given by Su = 120 and Sd = 90. The risk-free rate is given by 5%. (a) What is the payoff at maturity of the portfolio? (b) Calculate the "Delta"...
4. An Asian option is an option whose payoffs depend on the average price of the...
4. An Asian option is an option whose payoffs depend on the average price of the un- derlying asset over a certain period of time (instead of the price at maturity in the case of standard options). Early exercise of the option is not allowed. For instance, consider the payoff of an Asian Call option at maturity (in three months) on a stock ABC that does not pay dividends : Cz = max ( Si + S2 + S3 -...
g) European call with a strike price of $40 costs $7. European put with the same...
g) European call with a strike price of $40 costs $7. European put with the same strike price and expiration date costs $6. Assume that you buy two calls and one put (strap strategy). Sketch the graph and write down functions of payoff and profit h) Consider a stock with a price of $50 and there is European put option on that stock with the strike of $55 and premium of $4. Assume that you buy 1/3 of a stock...
Exercise 1. An investor has a short position in a European put on a share for $4. The stock price is $40 and the strike price is $41 Under what cicum be cuercise (b) Under what circumstance does the...
Exercise 1. An investor has a short position in a European put on a share for $4. The stock price is $40 and the strike price is $41 Under what cicum be cuercise (b) Under what circumstance does the investor make a profit? (c) Draw a payoff diagram plotting the investor's payoff as a function of Sr. (d) Draw a profit diagram plotting the investor's profit as a function of ST. (e) Suppose now the investor enters also into a...
4. Consider six months European put option with a strike price of $100 on a stock...
4. Consider six months European put option with a strike price of $100 on a stock with current price $100. There are two time steps and in each time step the stock price either moves up by 10% or moves down by 10%. Risk-free interest rate is Y-5% (on 3 months (a) Find the current option price. (b) Compute the number of shares of stock which should be held by the replicating portfolio at time 0 and 1 (after 3...
Suppose stock ABC is worth 100 at t=0 and there are two scenarios for the stock...
Suppose stock ABC is worth 100 at t=0 and there are two scenarios for the stock price at t=1 The stock price can go up to 110 The stock price can go down to 90 Now consider a PUT option on ABC with exercise price 100. In the portfolio of stock and zero coupon bond that replicates the payoff of the put option (the replicating portfolio), what is your position in ABC stock Select one: a. You are long 1/2...
You are attempting to formulate an investment strategy. In particular, you short a put option with strike price X1 equal...
You are attempting to formulate an investment strategy. In particular, you short a put option with strike price X1 equals to $95 and you long another put option with strike price X2 equals to $115. Both put options have the same underlying stock and will expire at time T. (a) Plot the payoff structure of this investment strategy as a function of ST, which stands for the price of the underlying stock at maturity. The X-axis for St and the...
1. Consider the following discrete time one-period market model. The savings account is given by Bo 1 and B1 1.1. The stock price is given by So 1 and S,-ξ where ξ is a random variable taking two possible values u 1.2 and d = 0.9. Consider a put option whose payoff at time l is P = (1-S)+. (a) Find a replicating strategy for this option. By considering the value of the replicating strategy, find the time 0 price...
2. Let Bt denote a Brownian motion. Consider the Black-Scholes model for the price of stock St, 2 So-1 and the savings account is given by β,-ea (a) Solve the equation for the price of the stock St and show that it is not a (b) Explain what is meant by an Equivalent Martingale Measure (EMM) martingale. State the Girsanov theorem. Give the expression for Bt under the EMM Q, hence derive the expression for St under the EMM, and...
please type your answer
4. Consider a portfolio consisting of 6 stocks and 10 put options on the stocks. The current stock price is So = 100 and the stike price of the options is X = 100. The stock price can take on only two values at maturity T given by Su = 120 and Sd = 90. The risk-free rate is given by 5%. (a) What is the payoff at maturity of the portfolio? (b) Calculate the "Delta"...
4. An Asian option is an option whose payoffs depend on the average price of the un- derlying asset over a certain period of time (instead of the price at maturity in the case of standard options). Early exercise of the option is not allowed. For instance, consider the payoff of an Asian Call option at maturity (in three months) on a stock ABC that does not pay dividends : Cz = max ( Si + S2 + S3 -...
g) European call with a strike price of $40 costs $7. European put with the same strike price and expiration date costs $6. Assume that you buy two calls and one put (strap strategy). Sketch the graph and write down functions of payoff and profit h) Consider a stock with a price of $50 and there is European put option on that stock with the strike of $55 and premium of $4. Assume that you buy 1/3 of a stock...
Exercise 1. An investor has a short position in a European put on a share for $4. The stock price is $40 and the strike price is $41 Under what cicum be cuercise (b) Under what circumstance does the investor make a profit? (c) Draw a payoff diagram plotting the investor's payoff as a function of Sr. (d) Draw a profit diagram plotting the investor's profit as a function of ST. (e) Suppose now the investor enters also into a...
4. Consider six months European put option with a strike price of $100 on a stock with current price $100. There are two time steps and in each time step the stock price either moves up by 10% or moves down by 10%. Risk-free interest rate is Y-5% (on 3 months (a) Find the current option price. (b) Compute the number of shares of stock which should be held by the replicating portfolio at time 0 and 1 (after 3...
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