6. Currency options

International Financial Services 2

Karel Bruna

Main Characteristics of Currency Options

Markets: OTC contract/exchange traded contract

Maturity: 1M, 2M, 3M, 6M, 9M, 12M + odd dates/fixed dates

Price: bid/ask option premium

Currency pairs: main currency pairs

Amount: minimum defined by the market maker/exchange

Interest Rates: interbank deposit/lending rates

yields of treasury instruments

Currency optionsUSD/EUR call option profit/loss function, SP = 1,20 USD/EUR, Pr = 0,1 USD/EUR

profit call option holder

0,1

1,20 1,40

future spot rate -0,1 1,30

call option writer

loss

Currency optionsoption premium

option premium = intrinsic value + time value

Currency optionsGarman and Kohlhagen pricing formula for European call (c) and put (p) options

where:

SR - actual spot exchange rate

SP - strike (exercise) price

IRD and IRF - domestic and foreign risk free interest rate

t - time (in years) until the expiration of the option

σ - volatility of spot exchange rate

Φ - standard normal cumulative distribution function

)d(SPe)d(ReSc 2tIR

1tIR DF

)d(ReS)d(SPep 1tIR

2tIR FD

t

t)2IRIR()SPSRlog(d

2FD

1

tdd 12

Range forward

put option holder asset

1,50 net position

24,50 26 27,70 29,20 0 - 0,20 26,20 SRt+n (CZK/EUR)

- 1,50 call option writer