(a) Draw 2-period binomial tree of your assets, assuming an asset volatility of
33.65% per year and the risk-free interest of 10% per annum.
(b) Will you exercise the option to maintain the assets?
2. EarBook Inc has issued a mandatory zero-coupon convertible bond. EarBook’s
asset value today is 100. Each period it can go up by u=1.25 or down by d=1/u.
The risk free rate is 5%.
(a) Draw the asset value tree of EarBook Inc.
(b) The mandatory convertible bond has to be converted into shares either at
t=1 or at t=2, which is the maturity date of the convertible. The fraction
of shares obtained after conversion is
γ
.
In contrast to normal convertible
bonds,
γ
depends on the value of assets. The following diagram displays the
time varying
γ
of the convertible.
γ
u
= 0
.
07
γ
d
= 0
.
12
γ
uu
= 0
.
06
γ
ud
= 0
.
10
γ
dd
= 0
.
14
t
= 0
t
= 1
t
= 2
1

What is the market value of this mandatory convertible bond today?
3. Use the put-call parity to derive, for a non-dividend paying stock, relationship
between:
(a) The delta of a European call and the delta of a European put
(b) The gamma of a European call and the gamma of a European put
4. Show that the delta (Δ), gamma (Γ) and theta (Θ) of a non-dividend paying call
option (call value
C
) satisfy the following equality:
Θ +
rS
0
Δ +
1
2
σ
2
S
2
0
Γ =
rC
Is the equation applicable for non-dividend paying put?
5. A company uses delta hedging to hedge a portfolio of long positions in put and
call options on a currency.
Which would give the most favorable result for the
portfolio (delta hedged): a virtually constant spot rate or wild movements in the
spot rate? Explain briefly
2

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