1 A large company carries out business in its home country, X, and in another country,

Y. Each country has a different currency. The company makes extensive use of a

commodity available to buy only in Country Y, which it purchases using the currency

of Country Y.

(i) Define a quanto option and give a suitable example based on the company and

the commodity described above. [4]

(ii) Assess the effectiveness for the company of using quanto options to attempt to

fully hedge the risks associated with the future buying of the commodity in the

commodity market. [6]

[Total 10]

2 (i) Define an exotic option. [1]

(ii) State the main differences between:

a cash-or-nothing binary put option; and

an asset-or-nothing binary call option.

[2]

An exotic option has an underlying asset with price S(t) at time t.

The underlying asset price process under the risk neutral measure P is given by

dS(t) = S(t)(r - q)dt + S(t)sdW(t), where r is the constant interest rate, q is the constant

dividend yield of the underlying asset, W(t) is P Brownian motion and s is the

constant volatility of the underlying asset price.

(iii) Write down an expression for S(T )|Ft

under the measure P, where Ft

is the

filtration. [2]

Suppose Q is a measure equivalent to P with Q Brownian motion WQ(t) and g = -2s

is an Ft

previsible process satisfying WQ(t) = W(t) + 0

t

gds.

(iv) Derive the stochastic differential equation for dS(t) and the expression for

S(T )|Ft, both under the measure Q. [3]

(v) Determine the Radon-Nikodym derivatives dQ

dP (which is P measurable) and

dP

dQ (which is Q measurable and noting dP

dQ

= dQ

dP

-1

). [3]

[Total 11]SP6 A2020-3 PLEASE TURN OVER

3 E-Coin is a recently launched digital currency that does not involve a central bank.

The number of E-Coins is currently limited, but new E-Coins are occasionally issued.

There is a cap on the total number of E-Coins that will likely be reached in a few

years. E-Coin is gaining in popularity and an established exchange is about to launch

an E-Coin future.

(i) Determine whether the E-Coin would be considered an investment asset or a

consumption asset. [2]

(ii) List the items that the exchange would need to specify in the E-Coin future.

[3]

The exchange is concerned that many of the E-Coin futures may be traded by less

experienced investors with limited financial resources for speculative purposes.

(iii) Describe the risks to the exchange of these less experienced investors trading

in the new E-Coin futures. [3]

(iv) Explain how the exchange can mitigate the risks described in part (iii). [3]