No-arbitrage pricing of FX forwards and options

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: $F_{p/b} = S_{p/b}e^{(r_p - r_b)T}$.
• 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.