Essay Calculate the Price of a European Call Option and Put Option – Management Assignment Help

Assignment Task:

Task:

1. A stock trades at $20. Its annual volatility is 18%. The risk-free rate is 3%. Calculate the price of a European call option and put option with strike K = 20 and T equal to 4 months.(Don’t need to do this one
2. (Continued) Calculate the ? of a portfolio consisting of 2 long calls and 1 short put from the previous problem. How many shares of the stock would you short in order to build a new portfolio that is delta-neutral?
5. (Continued) Calculate the ? and the ν of a straddle built from one of the calls and one of the puts. This example illustrates why a straddle built from at-the-mo

10. Assume the log-normal model. The spot price is $100. The expected rate of return is 10%.
The volatility is 20%. The risk-free rate is 3%. A “power derivative” pays you the square of the underlying asset price in 4 months. Calculate its ? and Γ today.
11. (Continued). Suppose the asset price jump up by $0.05 today. Use your computation of the ? to estimate the new price. Without computing the new price exactly, argue whether this is an underestimate or and overestimate, based on your computation for Γ. (Possibly Useless Hint: consider the parabola y = ax2 ; for what values of the constant a is the tangent-line approximation of the parabola at the origin an overestimate and for what values is it an underestimate?)

14. Consider the 2-step binomial tree from Problem 9 in Chapter 8. Compute the value of ? of the European put option at the initial node and each of the two intermediary nodes.
9. A stock price is currently $30. Every 6 months the price will either go up by 12% or down by 8%. The risk-free rate is 4% per annum with continuous compounding. (a) Compute the price of a one-year European put option with strike price $32. (b) Compute the price of a one-year American put option with strike price $32. (For problem 14)

15. (Continued) Build a portfolio consisting of cash (borrowed from or deposited in a bank at the risk-free rate), a certain amount of stocks, and 1 put option so that its value at the initial node is zero and so that its value will be zero regardless of where the stock goes at the intermediate time step.

16. (Continued) Suppose the stock goes up at the intermediate time step. What should your new portfolio holdings (1 put, some cash, and some stock) be so that its value will still be zero and so that its value at the final time step is also guaranteed to be zero. This is an example of dynamic hedging.