Financial Engineering Project Analysis Instructions :

A$.$ The current price of a non$-$dividend$-$paying stock is $$100.$ Over the next six months it is expected to rise to $$110$ or fall to $$95.$ Assume the risk$-$free rate is $5\%.$ An investor sells six$-$month call options with a strike price of $$100.$ How many shares does the investor need to buy for hedging the position?

B$.$ No dividend paid stock follows a $4-$step binomial tree process and the risk free rate is $5\%.$ Create a $4$ steps $($each step$=1$ month$)$ Binomial tree starting at stock price $$100$ with $1$ month up to $$105.$ Compute the stock prices for each node, the Arithmetic average prices for each node and the risk$-$neutral probability of an up movement $.$

C$.$Using the above $4$ step tree model, compute the stock volatility and Arithmetic European Asian Call option value at $4$ month maturity for the strike price $$100.$

D$.$Select a numerical procedure to analyze and price Arithmetic Europan Asian option, and describe the general framework with necessary steps to provide the numerical solution for Arithmetic European Asian option. The numerical procedures can be any tree models; monte carlo, finite difference or other approximations.

E$.$ No dividend paid stock follows a GBM with initial value S$=100$ and the volatility $15\%.$ Assume the option maturity is $1$ year, the strike price is $100$ and the risk free rate is $5\%.$ Compute the Arithmetic European Asian Call option value with the table and display as a graph and its Delta & Gamma $.$ You shall provide the codes and output files. You can use Excel, MatLab or other analytics.

$10+$ slides or pages