Spot an options arbitrage opportunity and set out the trades that exploit it
The idea
A mispriced option is exploited by trading it against its replicating portfolio. If a call trades above model value, sell it and buy h shares, financing part of the cost by borrowing. The hedged position has a riskless payoff but costs less than that payoff's present value, so the price gap is profit today. If the call trades below value, buy it, short h shares and lend. For American options another check applies: an option trading below its exercise value can be bought and exercised at once, a put together with buying the share. Parity violations work the same way: buy the cheap side, sell the dear side. The trap is getting the direction backwards, or measuring the gap against an undiscounted expected payoff.
In the app: 2 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
Take the free diagnostic →More in Valuation of Contingent Claims
- Explain the binomial model for valuing options and what each of its terms means
- Explain how a European option's value can be viewed as its expected payoff at expiry discounted to today
- Use a two-period binomial model to work out no-arbitrage values for American and European options
- Use a two-period binomial model to value an interest rate option and explain the result
- Name the assumptions behind the Black–Scholes–Merton model for valuing options
- Explain how the Black–Scholes–Merton call formula can be read as a leveraged holding of the underlying
- Explain how European options on currencies and equities are valued with the Black–Scholes–Merton model
- Explain how the Black model values European options on futures contracts
- Explain how the Black model values European swaptions and European interest rate options
- Explain what each option Greek measures
- Explain the steps in carrying out a delta hedge
- Explain why gamma risk matters when trading options
- Say what implied volatility is and how options traders use it