FNCE90011 Derivative Securities
3
Question 5
[replicating strategy for exotic derivative]
A stock is currently priced at $20. The volatility of the stock is 40% pa and the riskfree rate of
interest is 4% pa with continuous compounding. We model the possible movement of stock
price over the next 6 months using a one-step Binomial tree. This means that
u
= 1.3269 and
d
= 0.7536.
Let
S
T
denote the stock price 6 months from now. Define a new derivative security which has
a payoff equal to (
S
T
)
2
. That is, if you buy this derivative security today, in 6 months
'
time, you
will receive a cash payment equal to the square of stock price at the point.
How much will this derivative security sell for in the market today?
Hint: don't be distracted by the unusual nature of this derivative. It is not
an option. It doesn't
even have a strike price! Nevertheless, you can still use either of the methods from Lecture 8
to price the derivative (delta-hedging will be easier; try both methods if you are keen :).
Question 6
[Binomial price is only an approximation]
The current price of Coles Myer is $13. The standard deviation (
) of CML's return is 0.24 per
annum. A call option with six months to expiry has a strike price of $11. The riskless rate of
interest is 5% per annum continuously compounded.
a)
Use the Black-Scholes formula to price the call option. The implicit assumptions are
that it is a European-style option and that CML will not pay dividends during the next
six months.
b)
For a European call option, the Black-Scholes formula gives the exact price. In contrast,
the Binomial method only gives an approximation to the true Black-Scholes price. Use
a one-step Binomial tree to approximate the call option price.
c)
To get a more accurate approximation, we can use more steps in the Binomial tree. Use
a two-step tree to approximate the call option price.
Hint: in parts b and c, you will have to calculate the proportional up/down movements
using the volatility.