compound: Compound options

In derivmkts: Functions and R Code to Accompany Derivatives Markets

Compound options

Description

A compound option is an option for which the underlying asset is an option. The underlying option (the option on which there is an option) in turn has an underlying asset. The definition of a compound option requires specifying

• whether you have the right to buy or sell an underlying option

• whether the underlying option (the option upon which there is an option) is a put or a call

• the price at which you can buy or sell the underlying option (strike price kco — the strike on the compound option)

• the price at which you can buy or sell the underlying asset should you exercise the compound option (strike price kuo — the strike on the underlying option)

• the date at which you have the option to buy or sell the underlying option (first exercise date, t1)

• the date at which the underlying option expires, t2

Given these possibilities, you can have a call on a call, a put on a call, a call on a put, and a put on a put. The valuation procedure require knowing, among other things, the underlying asset price at which it will be worthwhile to acquire the underlying option.

Given the underlying option, there is a parity relationship: If you buy a call on a call and sell a call on a call, you have acquired the underlying call by paying the present value of the strike, kco.

Usage

binormsdist(x1, x2, rho)
optionsoncall(s, kuo, kco, v, r, t1, t2, d)
optionsonput(s, kuo, kco, v, r, t1, t2, d)
calloncall(s, kuo, kco, v, r, t1, t2, d, returnscritical)
callonput(s, kuo, kco, v, r, t1, t2, d, returnscritical)
putoncall(s, kuo, kco, v, r, t1, t2, d, returnscritical)
putonput(s, kuo, kco, v, r, t1, t2, d, returnscritical)

Arguments

s	Price of the asset on which the underlying option is written
v	Volatility of the underlying asset, defined as the annualized standard deviation of the continuously-compounded return
r	Annual continuously-compounded risk-free interest rate
d	Dividend yield of the underlying asset, annualized, continuously-compounded
kuo	strike on the underlying option
kco	strike on compound option (the price at which you would buy or sell the underlying option at time t1)
t1	time until exercise for the compound option
t2	time until exercise for the underlying option
x1, x2	values at which the cumulative bivariate normal distribution will be evaluated
rho	correlation between x1 and x2
returnscritical	(FALSE) boolean determining whether the function returns just the options price (the default) or the option price along with the asset price above or below which the compound option is exercised.

Value

The option price, and optionally, the stock price above or below which the compound option is exercised. The compound option functions are not vectorized, but the greeks function should work, apart from theta.

Note

The compound option formulas are not vectorized.

derivmkts documentation built on April 11, 2022, 5:10 p.m.