Math 238, Financial Mathematics
Problem set 2
January 27, 2009
These problems are due on Friday January 30, 5:00pm. You can give them to me in class, drop
them in my office, or put them in my mailbox outside the mathematics department. You will need
to use Matlab or some other computational tool in some of these problems.
Problem 1
Derive the putcall parity relation using the BlackScholes partial differential equation and then
give a detailed noarbitrage interpretation of it.
Problem 2
(a) Use the formula for the explicit solution of the BS equation to price one call option today,
where
S
(0) = $850, the strike time is three months, the strike price is
K
= $950, the volatility
is 40% and the interest rate is 1%. (b) Plot this price as a function of the volatility from 15% to
60%. (c) Calculate the hedge ratio one month before strike time for (a), for a range of
S
around
the strike price, and plot it. (d) What is the price of a put with the same parameters as (a)? (e)
What is the price of a put with parameters as in (a) except that
K
= $750? If you sell a call as in
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 Winter '08
 Papanicolaou
 Math, Options, Mathematical finance, Strike price, Stochastic volatility

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