30.
You are given the following market data for zero-coupon bonds with a maturity
payoff of $100.
Maturity (years)
1
2
Bond Price ($)
94.34
88.50
Volatility in Year 1
N/A
10%
A 2-period Black-Derman-Toy interest tree is calibrated using the data from abov
4. For a two-period binomial model, you are given:
(i)
Each period is one year.
(ii)
The current price for a nondividend-paying stock is 20.
(iii) u
1.2840, where u is one plus the rate of capital gain on the stock per period if
the stock price goes up.
(
5.
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You are given that:
(i)
The current exchange rate is 1.43 US dollars per pound.
(ii)
The strike price of the put is 1.56 US dollars per pound.
(iii) The volatility of the exch
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13.
Let cfw_Z(t) be a standard Brownian motion. You are given:
(i)
U(t)
2Z(t)
(ii)
V(t)
[Z(t)]2
(iii) W(t)
2
t
t
t2 Z(t) 2 sZ ( s)ds
0
Which of the processes defined above has / have zero drift?
(A) cfw_V(t) only
(B) cfw_W(t) only
(C) cfw_U(t) and cfw_V(t
18.
A market-maker sells 1,000 1-year European gap call options, and delta-hedges the
position with shares.
You are given:
(i)
Each gap call option is written on 1 share of a nondividend-paying stock.
(ii)
The current price of the stock is 100.
(iii) The
19.
Consider a forward start option which, 1 year from today, will give its owner a
1-year European call option with a strike price equal to the stock price at that time.
You are given:
(i)
The European call option is on a stock that pays no dividends.
(i
20.
Assume the Black-Scholes framework. Consider a stock, and a European call
option and a European put option on the stock. The current stock price, call price,
and put price are 45.00, 4.45, and 1.90, respectively.
Investor A purchases two calls and one
28.
Assume the Black-Scholes framework. You are given:
(i)
S(t) is the price of a nondividend-paying stock at time t.
(ii) S(0)
10
(iii) The stock s volatility is 20%.
(iv) The continuously compounded risk-free interest rate is 2%.
At time t 0, you write
29.
The following is a Black-Derman-Toy binomial tree for effective annual interest
rates.
Year 0
Year 1
Year 2
6%
5%
rud
r0
3%
2%
Compute the volatility in year 1 of the 3-year zero-coupon bond generated by the
tree.
(A)
14%
(B)
18%
(C)
22%
(D)
26%
(E)