Consider a put option on a stock that currently sells for £100, but may rise to £120 or fall to £80 after 1 year. The ri

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Consider a put option on a stock that currently sells for £100,
but may rise to £120 or fall to £80 after 1 year. The risk free
rate of return is 10%, and the exercise price is £90.
(a) Calculate the value of the put option using the risk-neutral
valuation relationship (RNVR). Explain the reasoning behind your
calculations. [10 marks]
(b) Calculate the value of the put option by using first
principles (No Arbitrage principles). Explain the reasoning behind
your calculations. [10 marks]
(c) What is the price of a call option on the same stock with
the same exercise price and the same expiration date? Explain the
reasoning behind your calculations. [10 marks]
(d) Is there an arbitrage opportunity in this market? Explain.
[10 marks]
(e) You expect little or no change in stock prices in the near
future. Construct as many option portfolios as you can to make some
profit. You can buy and sell as many options as you like with the
exercise price and expire date shown in parts (a)-(c). Sketch the
Profit and Loss graph for your portfolio and briefly explain. [10
marks]