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Let us consider an option on a dividend paying stock with dividend delta , volatility sigma , risk - free rate r over
Let us consider an option on a dividend paying stock with dividend
delta
volatility
sigma
risk
free rate r over a period
Delta t
a
Show that the risk
neutral
martingale
probability q can be written as:
q
e
r
delta
Delta t
e
sigma
Delta t
e
sigma
Delta t
e
sigma
Delta t
b
In a risk
neutral world, a future contract is treated as stock paying a continuous
dividend yield equal to the risk
free rate r
Deduce from question a
the risk
neutral
martingale
probability q expression for a future contract.
The current price of a eight
month future is
the risk
free rate is
the strike price
is
and the volatility is
per annum.
c
Use a two
step binomial tree to display the price process of the eight
month future
contract
Consider u
e
sigma
Delta t
d
e
sigma
Delta t
d
Use the two
step binomial tree defined in c
to calculate the value an eight
month
American put option on the future contract.
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