QFRM (version 1.0.1)

GapMC: Gap option valuation via Monte Carlo (MC) simulation

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

Usage

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.

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

(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