Lesson 8 of 8 · All lessons in this module
- Present value and discount (zero-coupon) bondsVideo lesson
- Coupon bonds and perpetual bonds
- Level-payment instruments: mortgages and amortizing loansVideo lesson
- Valuing shares with dividend discount models
- Implied returns on bonds
- Required return, implied growth and the P/E ratio
- Cash flow additivity, no arbitrage and forward rates
- No-arbitrage pricing of FX forwards and options
Lesson 8 of 8 · 15 min
No-arbitrage pricing of FX forwards and options
The same no-arbitrage logic sets forward exchange rates (two riskless deposits must end equal) and option values (a riskless share-plus-option portfolio must earn the risk-free rate).
In short
- Depositing in the base currency must equal converting at spot, depositing in the price currency and converting back at the forward rate.
- With continuous rates and price/base quotes: .
- The higher-rate currency trades at a forward discount; the lower-rate currency at a forward premium.
- One-period binomial model: combine shares and an option so the portfolio is worth the same whether the price goes up or down.
- Call: buy h shares and sell one call. Put: buy h shares and buy one put. Discount the riskless end value at r to get today's option price.
- The number of shares per option is the hedge ratio.
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