Question 2 Suppose stock A is currently traded at £100. In one year, its price will be either £110 or £90. The risk-free

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Question 2
Suppose stock A is currently traded at £100. In one year, its
price will be either £110 or £90. The risk-free interest rate is 5%
and the yield curve is flat.
a) What is the price of a put option with K=95 and expires in
one year?
(10 marks)
b) Suppose you entered a short position in a 1-year forward on
stock A at t=0. Three months later (t=0.25), the stock price is
still £100. What is the value of your position at t=0.25?
(10 marks)
c) Suppose you are a corporate treasurer, and you manage the
cash savings of your firm. You don’t want to lose any initial
investment and wish to make a return higher than the risk-free rate
in some cases. Your bank proposes a product that costs £100 and
delivers the following payoff in one year:
100×(1+0.8×max􁉄𝑆𝑆𝑇𝑇−100𝑆𝑆𝑇𝑇,0􁉅), i.e., this product guarantees you
never lose a penny and gives you 80% of ‘‘gain’’ if the stock price
appreciates. Will you invest in this product? Justify your answer
with calculations.
(10 marks)
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d) Will your answer to question c) change if in one year the
stock price will be either £120 or £80 (instead of £110 or £90)?
Justify your answer.
(10 marks)