# Finance-AW-Q419

## Finance-AW-Q419 Online Services

problem 1

the current price of a stock is S=20. It is known that at the end of 6 months the stock will be either Su= 24 or Sd=18.]

1. Compute the risk-neutral price of the call option with the strike price E=21 and r= 5%.
2. Show that there exists arbitrage if the price of the call option is below the risk-neutral price. Consider a particular example- the price of the Call option with the above parameter is C= 0.75.
Show the details for the arbitrage ( buy the call option and short-sell delta shares). Show details computations for the arbitrage for S(T) = 18 and S(T)= 24.

Problem 4

Assume that observations on a stock prive at the end of each 15 consecutive weeks are

30.2, 32, 31.1, 30.1, 30.2, 30.3, 30.6, 33, 32.9, 33, 33.5, 33.5, 33.7, 33.5, 33.2

Estimate the stock price volatility. Use trading days to estimate volatility. Number of trading days in a year = 252. Note: the time-step for observation is one calendar week, but you need to use trading days to compute the estimate. Use the log formula to express returns; use the unbiased estimator for the variance, take the mean into account when computing the volatility. Clearly write all the formulas you’re using.

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problem 5

Consider the following porfolio – buy a call and put options on the same asset with the same strike prive E.

i) Derive and plot the payoff function for this portfolio.
ii) Derive the final condition (time=expiry) and two boundary condition (S=0 and S –> infinity) for pricing with the Black-Scholes equation.

Product Code-Finance-AW-Q419