bs.opt: Black-Scholes Option

In johnlaing/bs.opt: Black-Scholes options

Description

Applications of he Black-Scholes option pricing formula

Usage

bs.opt(cp=c("call", "put"), strike=NULL, delta=NULL, time.to.mat=NULL, val.date=NULL, exp.date=NULL, spot, vol=NULL, price=NULL, rate=NULL, fwd=NULL)
bs.fx.opt(cp=c("call", "put"), strike=NULL, delta=NULL, time.to.mat=NULL, val.date=NULL, exp.date=NULL, spot, vol, rate=NULL, fwd=NULL)

Arguments

cp	Direction of the option: call or put.
strike	Strike price of the option. If left NULL, will be calculated from delta.
delta	Delta of the option. Used to calculate the strike if strike is NULL, and ignored otherwise.
time.to.mat	Time to maturity of the option, expressed in years. If left NULL, will be calculated from val.date and exp.date.
val.date, exp.date	Valuation and expiration dates. Used to calculate time to maturity if time.to.mat is NULL, and ignored otherwise.
spot	Spot price of the underlying.
vol	Volatility of the underlying.
price	Price of the option.
rate	Risk-free or forward rate. If left NULL, will be implied from fwd, spot, and time.to.mat.
fwd	Forward price of the underlying. Used to calculate forward rate if rate is NULL, and ignored otherwise.

Details

These functions take inputs necessary for evaluating options and run them through the Black-Scholes formula and its derivatives. The bs.fx.opt variant implements the conventions of FX options that are priced in the currency of the underlying. E.g., a EUR/USD option (the option to buy or sell EUR vs USD) is priced in EUR. In this function:

P' = P/S \\ Δ' = dP'/dS * S = Δ - P' \\ Γ' = dΔ'/dS = Γ - Δ'/S

Value

A data.frame with inputs, price, and sensitivities.

References

http://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model

Examples

## puts on SPX
bs.opt("put", strike=seq(1940, 1960, 5), time.to.mat=63/365, spot=1960, vol=0.025, fwd=1954)

## use dates instead of time.to.mat
today <- Sys.Date()
bs.opt("put", strike=seq(1940, 1960, 5), val.date=today, exp.date=today+63, spot=1960, vol=0.025, rate=0.0197)

## EUR/USD -- use fwd instead of rate
bs.fx.opt("call", strike=135:138/100, val.date=today, exp.date=today+365, spot=1.365, vol=0.07, fwd=1.365)

## back into strikes from deltas
bs.fx.opt(c("put", "put", "call", "call"), delta=c(-.25, -.50, .50, .25), time.to.mat=0.25, spot=1.365, vol=0.05, rate=0)

johnlaing/bs.opt documentation built on May 19, 2019, 5:15 p.m.