# Derivative Securities Assignment Harvard Case Solution & Analysis

## Case Solution

Question 1

a)
The theoretical price of the call is given by the put-call parity as follows:
c=p-kxexp(-rT)+Soxexp(-qT)

c = 5.44826

b).
As seen by the above theoretical price of call, the call is underpriced in the market. Therefore, in order to make an arbitrage opportunity one must buy the call, sell index and then buy call again. The arbitrage details would be as follows:

Today

Sell the 6 months put at \$ 3.2
Short exp(-qt) units of the index at \$ 61.21exp(-4%*0.5) = \$ 59.998
Buy the 6 months call at \$ 4.95 and invest all the net proceeds of 3.2+59.998-4.95= 58.248 so the net cash flows today become 0.

One unit of St is bought at index and the investment grows to 58.248*exp(4%*0.5) = 59.4247
The net cash flow at maturity is \$ 1.17669.
c).
If we check that C-P = \$ 4.95-3.2 = \$ 1.75
No arbitrage bounds here are:
S0 x exp(-qT) – K ≤ C – P ≤ S0 – K x exp(-rT)
Or -29.245<= C-P<= 2.39
So there is no arbitrage opportunity.......................

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