What are the major determinants of the value of a currency option (call and put)?
a. Briefly justify each determinant and its direction.
b. What is the relation between a currency put and a currency call (put-call parity)?
c. In what circumstances would an American-type option be exercised before expiration?
(You may provide an example to illustrate your answers.)

Question

Quizplus · Accepted Answer

The Answer is a. The main determinants of the value of a currency option are listed below. As an illustration, we consider options quoted in dollar (domestic currency) on the Swiss franc (foreign currency). For example, a call SFr gives the option to buy one SFr at a prespecified dollar value (for example, 0.7 $/SFr).
$a. The main determinants of the value of a currency option are listed below. As an illustration, we consider options quoted in dollar (domestic currency) on the Swiss franc (foreign currency). For example, a call SFr gives the option to buy one SFr at a prespecified dollar value (for example, 0.7 $/SFr). b. Let's denote C the dollar premium of a call on the SFr with a strike K ($/SFr) P the dollar premium of a put on the SFr with a strike K ($/SFr) So the spot exchange rate ($/SFr) rSFr the Swiss franc interest rate r$ the U.S. dollar interest rate By arbitrage, we must have the put-call parity: P = C + \frac { K } { 1 + r _ { \$ } } - \frac { S _ { 0 } } { 1 + r _ { \mathrm { SFr } } } . c. An American call SFr is likely to be exercised before maturity when it is in-the-money and the SFr interest rate is high (relative to the $ interest rate). An American put SFr is likely to be exercised before maturity when it is in-the-money and the $ interest rate is high (relative to the SFr interest rate).$ b. Let's denote
C the dollar premium of a call on the SFr with a strike K ($/SFr)
P the dollar premium of a put on the SFr with a strike K ($/SFr)
S_o the spot exchange rate ($/SFr)
r_SFr the Swiss franc interest rate
r_$ the U.S. dollar interest rate
By arbitrage, we must have the put-call parity:

P = C + \frac { K } { 1 + r _ { \$ } } - \frac { S _ { 0 } } { 1 + r _ { \mathrm { SFr } } }

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c. An American call SFr is likely to be exercised before maturity when it is in-the-money and the SFr interest rate is high (relative to the $ interest rate).
An American put SFr is likely to be exercised before maturity when it is in-the-money and the $ interest rate is high (relative to the SFr interest rate).

What Are the Major Determinants of the Value of a Currency