# GapMC: Gap option valuation via Monte Carlo (MC) simulation In QFRM: Pricing of Vanilla and Exotic Option Contracts

## Description

GapMC prices a gap option using the MC method. The call payoff is S_T-K when S_T>K2, where K_2 is the trigger strike. The payoff is increased by K_2-K, which can be positive or negative. The put payoff is K-S_T when S_T<K_2. Default values are from policyholder-insurance example 26.1, p.601, from referenced OFOD, 9ed, text.

## Usage

 ```1 2 3 4``` ```GapMC(o = OptPx(Opt(Style = "Gap", Right = "Put", S0 = 5e+05, K = 4e+05, ttm = 1, ContrSize = 1, SName = "Insurance coverage example #26.1, p.601, OFOD, J.C.Hull, 9ed."), r = 0.05, q = 0, vol = 0.2), K2 = 350000, NPaths = 5) ```

## Arguments

 `o` The `OptPx` object (See `OptPx()` constructor for more information) `K2` The trigger strike price. `NPaths` The number of paths (trials) to simulate.

## Value

An `OptPx` object. The price is stored under `o\$PxMC`.

## Author(s)

Kiryl Novikau, Department of Statistics, Rice University, Spring 2015

## References

Hull, John C., Options, Futures and Other Derivatives, 9ed, 2014. Prentice Hall. ISBN 978-0-13-345631-8. http://www-2.rotman.utoronto.ca/~hull/ofod/index.html. p.601

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```(o = GapMC())\$PxMC #example 26.1, p.601 o = Opt(Style='Gap', Right='Call', S0=50, K=40, ttm=1) o = OptPx(o, vol=.2, r=.05, q = .02) (o = GapMC(o, K2 = 45, NPaths = 5))\$PxMC o = Opt(Style='Gap', Right='Call', S0 = 50, K = 60, ttm = 1) o = OptPx(o, vol=.25,r=.15, q = .02) (o = GapMC(o, K2 = 55, NPaths = 5))\$PxMC o = Opt(Style='Gap', Right = 'Put', S0 = 50, K = 57, ttm = .5) o = OptPx(o, vol = .2, r = .09, q = .2) (o = GapMC(o, K2 = 50, NPaths = 5))\$PxMC o = Opt(Style='Gap', Right='Call', S0=500000, K=400000, ttm=1) o = OptPx(o, vol=.2,r=.05, q = 0) (o = GapMC(o, K2 = 350000, NPaths = 5))\$PxMC ```

QFRM documentation built on May 29, 2017, 10:12 p.m.