89 lines
2.6 KiB
Go
89 lines
2.6 KiB
Go
package main
|
|
|
|
import (
|
|
"math"
|
|
"math/rand"
|
|
"time"
|
|
)
|
|
|
|
// Option struct that holds all the details of an option
|
|
type Option struct {
|
|
OptType int64
|
|
Strike float64
|
|
ExpiryDate time.Time
|
|
|
|
// Market data
|
|
ValueDate time.Time
|
|
Spot float64
|
|
Rfr float64
|
|
Vol float64
|
|
Sims int64
|
|
|
|
// Results
|
|
FV float64
|
|
Delta float64
|
|
Vega float64
|
|
Rho float64
|
|
Gamma float64
|
|
Theta float64
|
|
Levels []float64
|
|
}
|
|
|
|
// Single simulation of Geometric Brownian Motion
|
|
func gbmSimulation(spot float64, rfr float64, vol float64, tte float64, randNum float64) float64 {
|
|
var drift, stoch float64
|
|
|
|
drift = (rfr - math.Pow(vol, 2)/2) * tte
|
|
stoch = vol * math.Pow(tte, 0.5) * randNum
|
|
return spot * math.Exp(drift+stoch)
|
|
}
|
|
|
|
// PriceMonteCarlo is the exported method to run the simulations and value
|
|
// a vanilla option using Monte Carlo methods
|
|
func (opt *Option) PriceMonteCarlo() {
|
|
var i int64
|
|
var level float64
|
|
|
|
opt.Levels = make([]float64, opt.Sims)
|
|
|
|
tte := opt.ExpiryDate.Sub(opt.ValueDate).Hours() / (24 * 365)
|
|
|
|
for i = 0; i < opt.Sims; i++ {
|
|
randNum := rand.NormFloat64()
|
|
// Base
|
|
opt.Levels[i] = gbmSimulation(opt.Spot, opt.Rfr, opt.Vol, tte, randNum)
|
|
opt.FV += math.Max((opt.Levels[i]-opt.Strike)*float64(opt.OptType), 0)
|
|
|
|
// Delta
|
|
level = gbmSimulation(opt.Spot+0.0001, opt.Rfr, opt.Vol, tte, randNum)
|
|
opt.Delta += math.Max((level-opt.Strike)*float64(opt.OptType), 0)
|
|
|
|
// Gamma -- TODO: Doesn't look right
|
|
level = gbmSimulation(opt.Spot+0.0001, opt.Rfr, opt.Vol, tte, randNum)
|
|
level += gbmSimulation(opt.Spot-0.0001, opt.Rfr, opt.Vol, tte, randNum)
|
|
level -= 2 * gbmSimulation(opt.Spot, opt.Rfr, opt.Vol, tte, randNum)
|
|
opt.Gamma += math.Max((level-opt.Strike)*float64(opt.OptType), 0)
|
|
|
|
// Vega
|
|
level = gbmSimulation(opt.Spot, opt.Rfr, opt.Vol+0.0001, tte, randNum)
|
|
opt.Vega += math.Max((level-opt.Strike)*float64(opt.OptType), 0)
|
|
|
|
// Theta
|
|
level = gbmSimulation(opt.Spot, opt.Rfr, opt.Vol, tte-1./365, randNum)
|
|
opt.Theta += math.Max((level-opt.Strike)*float64(opt.OptType), 0)
|
|
|
|
// Rho -- TODO: Doesn't look right
|
|
level = gbmSimulation(opt.Spot, opt.Rfr+0.0001, opt.Vol, tte, randNum)
|
|
opt.Rho += math.Max((level-opt.Strike)*float64(opt.OptType), 0)
|
|
}
|
|
|
|
df := math.Exp(-opt.Rfr * tte)
|
|
opt.FV = opt.FV / float64(opt.Sims) * df
|
|
opt.Delta = (opt.Delta/float64(opt.Sims)*df - opt.FV) / 0.0001
|
|
opt.Gamma = (opt.Gamma/float64(opt.Sims)*df - opt.FV) / 10000
|
|
opt.Vega = (opt.Vega/float64(opt.Sims)*df - opt.FV) / 0.01
|
|
opt.Theta = (opt.Theta/float64(opt.Sims)*math.Exp(-opt.Rfr*(tte-1./365)) - opt.FV) / -(1. / 365)
|
|
opt.Rho = (opt.Rho/float64(opt.Sims)*math.Exp(-(opt.Rfr+0.01)*tte) - opt.FV)
|
|
}
|
|
|