compound {derivmkts}R Documentation

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

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.


[Package derivmkts version 0.2.4 Index]