Options Pricing Suite

Options that give the right to buy or sell the underlying asset at the strike price, without exotic features.

European option

Options may be exercised only at expiration.

American option

Options may be exercised at any time before or at expiration.

Stochastic volatility option

European options, with volatility following a random process.

Implied volatility

Given the option price, find the corresponding volatility.

Strategies involving combinations of vanilla options.

Bull spread

Long one call (put) at a lower strike and short another call (put) at a higher strike, with the same maturity.

Used when anticipating price increases.

Bear spread

Long one call (put) at a higher strike and short another call (put) at a lower strike, with the same maturity.

Used when anticipating price decreases.

Straddle

Long one call and one put with the same strike and maturity.

Used when anticipating large price movement in either direction.

Strangle

Long one call at a higher strike and one put at a lower strike, with the same maturity.

Used when anticipating large price movement (greater than when using a straddle) in either direction.

Butterfly spread

Long two options with different strikes and short two options at the midpoint strike, with the same maturity.

Used when anticipating only minimal price movement in either direction.

Condor spread

Long two options with different strikes and short two options at strikes in between, with the same maturity.

Used when anticipating only minimal price movement in either direction, with more flexibility than a butterfly spread.

Strip/strap

Long one call (put) and two puts (calls), with the same strike and maturity.

Used when anticipating large price movement in either direction, with a decrease (strip) or an increase (strap) more likely.

Front spread

Long one call at a lower strike and short two calls at a higher strike, or short two puts at a lower strike and long one put at a higher strike, with the same maturity.

Back spread

Short one call at a lower strike and long two calls at a higher strike, or long two puts at a lower strike and short one put at a higher strike, with the same maturity.

Option payoff depends on the average underlying asset price during the life of the option. Strike is fixed.

Arithmetic Asian option

Averaging is arithmetic: (x1+x2+x3+…+xn)/n.

Geometric Asian option

Averaging is geometric: (x1*x2*x3*…*xn)^(1/n)

Option payoff depends on the maximum or minimum underlying asset price during the life of the option.

Floating-strike lookback option

Call holder can buy the underlying at the lowest price observed during the life of the option. Payoff at expiration is
(Spot - Min spot).

Put holder can sell the underlying at the highest price observed during the life of the option. Payoff at expiration is
(Max spot - Spot).

Fixed-strike lookback option

Strike is fixed, but option exercise is not at the market price.

Call holder can exercise at the highest underlying price observed during the life of the option. Payoff at expiration is
max(Max spot - Strike,0).

Put holder can exercise at the lowest underlying price observed during the life of the option. Payoff at expiration is
max(Strike - Min spot,0).

Option payoff depends on whether the underlying asset price hits the barrier price level.

Single barrier option

Option activates or expires if the underlying price crosses the specified barrier level.

Double barrier option

Option activates or expires if the underlying price drops below the lower barrier or exceeds the upper barrier.

May be inaccurate when the strike is outside of the barrier range.

Option payoff is a specified amount if it expires in the money, or nothing if it expires out of the money.

Cash-or-nothing option

If in the money, option pays a fixed cash amount at expiration.

Calls pay the cash payment if
(Spot > Strike), otherwise nothing.

Puts pay the cash payment if
(Spot < Strike), otherwise nothing.

Asset-or-nothing option

If in the money, option pays the value of the underlying asset at expiration.

Calls pay the value of the asset if
(Spot > Strike), otherwise nothing.

Puts pay the value of the asset if
(Spot < Strike), otherwise nothing.

Gap option

European option with two strikes. The stated strike determines whether a payoff occurs, and the payoff strike determines the amount of the payoff. Payoff may be negative.

Calls pay
(Spot - Payoff strike) if
(Spot > Stated strike), otherwise nothing.

Puts pay
(Payoff strike - Spot) if
(Spot < Stated strike), otherwise nothing.

Options that combine the features of barrier options and binary options.

Cash-or-nothing payoff

Option pays out a fixed cash amount if the barrier condition is met. Payment can be made when the barrier event occurs or at maturity of the option.

Asset-or-nothing payoff

Option pays out the value of the underlying asset if the barrier condition is met. Payment can be made when the barrier event occurs or at maturity of the option.

Cash-or-nothing option

Option pays out a fixed cash amount if the barrier and strike conditions are met. Payment is made at maturity of the option.

Asset-or-nothing option

Option pays out the value of the underlying asset if the barrier and strike conditions are met. Payment is made at maturity of the option.

Double barrier binary

Option pays out a fixed cash amount depending on whether the spot price remains in or exits the barrier range. Payment is made at maturity of the option.

Asymmetric barrier option

Option pays out a fixed cash amount immediately if one barrier is hit, or expires if the other barrier is hit.

Supershare

If the spot price at maturity is within the barrier range, the payment made is the ratio
(Spot / Lower barrier), otherwise nothing.

European options whose underlying asset is another European option.

Option on a call

European option on a European call option.

Option on a put

European option on a European put option.

Option payoff depends on a power or logarithm of the spot and/or strike price.

Power contract

Payoff at maturity is (Spot / Strike)^Power.

Power option

Payoff at maturity depends on (Spot)^Power and can be capped.

Powered option

Payoff at maturity depends on a power of the difference of the spot price and strike price.

Log contract

Payoff at maturity is ln(Spot).

Log contract (ratio)

Payoff at maturity is ln(Spot / Strike). Payoff may be negative.

Log option

Payoff at maturity is max[ln(Spot/Strike),0].

Miscellaneous exotic options on a single underlying asset.

Chooser option

At the maturity of the option (the choice time), the holder can choose to receive a call option or a put option, each with a pre-specified strike and future maturity.

Payoff at the choice time is
max(Call price,Put price).

Accrual option

During the life of the option, the holder accrues a cash amount for each day the spot price is above or below the strike price. The payment of these accruals is made at maturity.

Exotic options that depend on two underlying assets.

Two-asset barrier option

Barrier option for which the price of asset 2 is linked to barrier hits, while the price of asset 1 is compared with the strike to determine the payoff.

Two-asset binary option

Cash-or-nothing option whose payoff depends on the prices and strikes of the two assets.

Min/max option

Option payoff at expiration depends on the lower or higher of the two asset prices.

Spread option

Option payoff at expiration depends on the difference between the prices of asset 1 and asset 2.

Exchange option

At expiration, the option holder can exchange asset 2 for asset 1.

Payoff at maturity is
max(Quantity 1*Spot 1 - Quantity 2*Spot 2,0).

Correlation option

At expiration, the spot/strike relationship for asset 1 determines the moneyness, while the spot/strike relationship for asset 2 determines the payoff amount.

Product option

Option payoff at expiration depends on the product of the prices of asset 1 and asset 2.

Quotient option

Option payoff at expiration depends on the ratio of the prices of asset 1 and asset 2.

Options involving foreign currencies.

Quanto option

Option price is in the domestic currency, while the underlying price and strike price are in the foreign currency.

Foreign equity option

Option price and strike price are in the domestic currency, while the underlying price is in the foreign currency.

Equity-linked FX option

Option on the exchange rate, linked to the forward price of a foreign equity or equity index.

Options involving interest rate dependency.

Bond option

European option on a zero coupon bond, using a Vasicek framework.

Caplet / floorlet

European option on the forward interest rate.

Swaption

Gives the right to enter into the underlying interest rate swap.