156 lines
4.4 KiB
Go
156 lines
4.4 KiB
Go
package main
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import (
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"fmt"
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"math"
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"math/rand"
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"time"
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)
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// RFC8601Time is a time.Time wrapper
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type RFC8601Time struct {
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time.Time
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}
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func (t RFC8601Time) Sub(u RFC8601Time) time.Duration {
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return t.Sub(u)
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}
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func (t RFC8601Time) MarshalJSON() ([]byte, error) {
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fmt.Println("Here!")
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stamp := fmt.Sprintf("\"%s\"", t.Format("2006-01-02"))
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return []byte(stamp), nil
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}
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// Option struct that holds all the details of an option
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// Option details
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type Option struct {
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optType int64
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strike float64
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expiryDate RFC8601Time
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// Market data
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valueDate RFC8601Time
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spot float64
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rfr float64
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vol float64
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sims int64
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// Results
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fv float64
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delta float64
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vega float64
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rho float64
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gamma float64
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theta float64
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}
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// Single simulation of Geometric Brownian Motion
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func gbmSimulation(spot float64, rfr float64, vol float64, tte float64, randNum float64) float64 {
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var drift, stoch float64
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drift = (rfr - math.Pow(vol, 2)/2) * tte
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stoch = vol * math.Pow(tte, 0.5) * randNum
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return spot * math.Exp(drift+stoch)
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}
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// RunSimulations is the main function that runs Monte Carlo simulations
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// for an option. Note that it runs normal Geometric Brownian Motion
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// to calculate the future spot levels
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func RunSimulations(opt *Option) {
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var i int64
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var level float64
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levels := make([]float64, opt.sims)
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tte := opt.expiryDate.Sub(opt.valueDate).Hours() / (24 * 365)
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for i = 0; i < opt.sims; i++ {
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randNum := rand.NormFloat64()
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// Base
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levels[i] = gbmSimulation(opt.spot, opt.rfr, opt.vol, tte, randNum)
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opt.fv += math.Max((levels[i]-opt.strike)*float64(opt.optType), 0)
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// Delta
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level = gbmSimulation(opt.spot+0.0001, opt.rfr, opt.vol, tte, randNum)
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opt.delta += math.Max((level-opt.strike)*float64(opt.optType), 0)
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// Gamma -- TODO: Doesn't look right
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level = gbmSimulation(opt.spot+0.0001, opt.rfr, opt.vol, tte, randNum)
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level += gbmSimulation(opt.spot-0.0001, opt.rfr, opt.vol, tte, randNum)
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level -= 2 * gbmSimulation(opt.spot, opt.rfr, opt.vol, tte, randNum)
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opt.gamma += math.Max((level-opt.strike)*float64(opt.optType), 0)
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// Vega
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level = gbmSimulation(opt.spot, opt.rfr, opt.vol+0.0001, tte, randNum)
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opt.vega += math.Max((level-opt.strike)*float64(opt.optType), 0)
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// Theta
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level = gbmSimulation(opt.spot, opt.rfr, opt.vol, tte-1./365, randNum)
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opt.theta += math.Max((level-opt.strike)*float64(opt.optType), 0)
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// Rho -- TODO: Doesn't look right
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level = gbmSimulation(opt.spot, opt.rfr+0.0001, opt.vol, tte, randNum)
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opt.rho += math.Max((level-opt.strike)*float64(opt.optType), 0)
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}
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df := math.Exp(-opt.rfr * tte)
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opt.fv = opt.fv / float64(opt.sims) * df
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opt.delta = (opt.delta/float64(opt.sims)*df - opt.fv) / 0.0001
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opt.gamma = (opt.gamma/float64(opt.sims)*df - opt.fv) / 10000
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opt.vega = (opt.vega/float64(opt.sims)*df - opt.fv) / 0.01
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opt.theta = (opt.theta/float64(opt.sims)*math.Exp(-opt.rfr*(tte-1./365)) - opt.fv) / -(1. / 365)
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opt.rho = (opt.rho/float64(opt.sims)*math.Exp(-(opt.rfr+0.01)*tte) - opt.fv)
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}
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/*
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func main() {
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value := time.Date(2016, 12, 30, 0, 0, 0, 0, time.UTC)
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expiry := time.Date(2017, 12, 30, 0, 0, 0, 0, time.UTC)
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opt := Option{optType: 1, strike: 100, expiryDate: expiry, valueDate: value, spot: 100, rfr: 0.03, vol: 0.25, sims: 1000000}
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rand.Seed(time.Now().UTC().UnixNano())
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RunSimulations(&opt)
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fmt.Printf(
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`
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Valuation date: %s
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| BS Analytic | BS Monte Carlo |
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---------------------------------------------
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|Type: | %10s | %13s |
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|Spot: | %10.2f | %13.2f |
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|Expiry: | %s | %s |
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|Strike: | %10.2f | %13.2f |
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|Risk-free: | %10.2f%% | %13.2f%% |
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|Implied Vol:| %10.2f%% | %13.2f%% |
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---------------------------------------------
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|Fair value: | %8.4f | %11.4f |
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|Delta: | %8.4f | %11.4f |
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|Gamma: | %8.4f | %11.4f |
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|Vega: | %8.4f | %11.4f |
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|Theta: | %8.4f | %11.4f |
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|Rho: | %8.4f | %11.4f |
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|Simulations:| | %11d |
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---------------------------------------------
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`,
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value.Format("2006-01-02"),
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"Call", "Call",
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opt.spot, opt.spot,
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expiry.Format("2006-01-02"), expiry.Format("2006-01-02"),
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opt.strike, opt.strike,
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opt.rfr*100, opt.rfr*100,
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opt.vol*100, opt.vol*100,
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opt.fv, opt.fv,
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opt.delta, opt.delta,
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opt.gamma, opt.gamma,
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opt.vega, opt.vega,
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opt.theta, opt.theta,
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opt.rho, opt.rho,
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opt.sims)
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}
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*/
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