int finc topic 5

• Currency Options:

derivative contracts giving their holder
the right (but not the obligation) to trade a currency at a
predetermined date in the future at a prearranged price,
regardless of market price of underlying currency traded

call optoin

right to buy

put option

right to sell

eu option

exercised on maturity

us option

exercised anytime until maturity

holder of a call option

(who is long the call) has the right to buy
FC in exchange for a certain number of units of HC from the counter-
party (the writer of the option; who is short the call) for a certain
price (the exercise or strike price

advantage of call

allows you to pay no more than the strike
price; and possibly less than the strike price

put option

contract that gives the holder (long the put) the right (but
not the obligation) to sell in the future a certain number of units of FC
in exchange for a certain number of units of HC from the counter-
party (the writer of the option, short the put)

advantage of put option

allows you to receive on maturity no less
than the strike price; and possibly more than the strike price

Intrinsic Value

the value you would receive if you
exercise the option now

Time Value

Since the intrinsic value of an out-of-the money option is zero, its price
represents exclusively time value
. may change to in the money with favourable spot changes

Total option value (option market price) =

Intrinsic value + Time value

Institutional Aspects of Options

• traded in clearing house

• have specific expiration dates

• contract sizes standardised

• OTC (written at the money)

For arbitrage opportunities, one should obtain:

✓(at zero initial cost) Positive cash flow and never worse than zero
✓(at negative initial cost) Cash flow never worse than zero

arbitrage

1. Options premia are non-negative (final payoff would always be, at
   the worst case, zero); this holds for both types of options

2. American Style options are worth no less than the European
   option

3. A European call/put is worth more than the comparable forward
   purchase/sale (since negative payoff is non-existent)

4. An American style call/put is worth at least its intrinsic value

5. Put-call parity for European style option

put call parity

• only for eu options

• if one more expensive then arb

P+St/(1+r*t,T)=C +X/(1+rt,T)

synthetic put

forward sale + call

using options for hedging

Options can be used to hedge cash flows denominated in foreign currency
certain to take place in the future; either
• Short position in FC
• Long position in FC

speculator

disagree with the market’s perceived probability distribution function for an
asset’s future value
• is willing to back his view with his/her own money

• prefer options as will only lose paid premium

A speculator may disagree with the view of the market regarding the
future exchange rate implied by the current forward rate. In that case

Call options can be used by speculators who bet on an appreciation of the
foreign currency (i.e. depreciation of the domestic currency)
• Put options can be used by speculators who bet on a deprec