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from navaidya

package net.gadgil.cgoptprice

import org.apache.commons.math3.distribution.NormalDistribution

import scala.collection.JavaConversions._

import org.apache.commons.math3.stat.descriptive.moment.StandardDeviation

object BlackScholes {

def d1d2(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

volatility: Double) = {

val d1 = (math.log(stockPrice / strikePrice) +

  (discountRate + math.pow(volatility, 2) / 2) * timeToExpiry) / (volatility * math.sqrt(timeToExpiry))

//Console.println(d1)

val d2 = d1 - volatility * math.sqrt(timeToExpiry)

(d1, d2)

}

/**

  • Black Scholes call option price

  • @param stockPrice - current price of the underlying stock

  • @param strikePrice - option strike price

  • @param timeToExpiry - option time to expiry

  • @param discoutRate - the discount rate. Normally the risk free rate

  • @param volatility - the volatility of the price

*/

def callOption(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

volatility: Double) = {

val (d1, d2) = d1d2(stockPrice, strikePrice, timeToExpiry, discountRate, volatility)

stockPrice * CND(d1) -

  strikePrice * math.exp(-discountRate * timeToExpiry) * CND(d2)

}

/**

  • Black Scholes put option price

  • @param stockPrice - current price of the underlying stock

  • @param strikePrice - option strike price

  • @param timeToExpiry - option time to expiry

  • @param discoutRate - the discount rate. Normally the risk free rate

  • @param volatility - the volatility of the price

*/

def putOption(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

volatility: Double) = {

val (d1, d2) = d1d2(stockPrice, strikePrice, timeToExpiry, discountRate, volatility)

strikePrice * math.exp(-discountRate * timeToExpiry) * CND(-d2) - stockPrice * CND(-d1)

}

/**

  • Generalized Black Scholes European call option paying a continuous dividend yield

  • Can be used to price European options on stocks with continuous dividend yield, options on futures and currency options

  • @param costOfCarry - Cost of carry

  • set this to discountRate for regular Black-Scholes price

  • set this to (discountRate - dividendYield) - for stocks with continuous dividend yield

  • set this to 0 for the Black-Scholes futures option

  • set this to (discountRate - discountRateInForeignCurrency) for currency option

*/

def callOptionGeneralizedBlackScholes(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

stockPrice * math.exp((costOfCarry - discountRate) * timeToExpiry) * CND(d1) - strikePrice * math.exp(-discountRate * timeToExpiry) * CND(d2)

}

/**

  • Generalized Black Scholes European put option paying a continuous dividend yield

  • Can be used to price European options on stocks with continuous dividend yield, options on futures and currency options

  • @param costOfCarry - Cost of carry

  • set this to discountRate for regular Black-Scholes price

  • set this to (discountRate - dividendYield) - for stocks with continuous dividend yield

  • set this to 0 for the Black-Scholes futures option

  • set this to (discountRate - discountRateInForeignCurrency) for currency option

*/

def putOptionGeneralizedBlackScholes(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

strikePrice * math.exp(-discountRate * timeToExpiry) * CND(-d2) - stockPrice * math.exp((costOfCarry - discountRate) * timeToExpiry) * CND(-d1)

}

def callOptionDelta(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

math.exp(1.0)

}

/**

  • Calculate the price volatility.

  • @param dataSeries - typically contains the daily prices

  • @param numPeriods - the number of periods to calculate the volatility. Usually 252 for the number of trading days in a year

*/

def volatility(dataSeries: Seq[Double], numPeriods: Double) = {

def percentChangeSeries(dataSeries: Seq[Double]) = {

  def percentChange(oldValue: Double, newValue: Double) = {

    (oldValue - newValue) / oldValue

  }

  (1 until dataSeries.length) map { i =>

    percentChange(dataSeries(i - 1), dataSeries(i))

  }

}



val changeSeries = percentChangeSeries(dataSeries)

val theStdDev = new StandardDeviation()

theStdDev.evaluate(dataSeries.toArray) * math.sqrt(numPeriods)

}

/**

  • Cumulative normal distribution value

*/

def CND(X: Double) = {

val theNormalDistribution = new NormalDistribution

theNormalDistribution.cumulativeProbability(X)

}

/**

  • fast approximation of the cumulative normal distribution function

*/

def CNDApprox(X: Double) = {

val a1 = 0.31938153

val a2 = -0.356563782

val a3 = 1.781477937

val a4 = -1.821255978

val a5 = 1.330274429



val L = Math.abs(X);

val K = 1.0 / (1.0 + 0.2316419 * L);

var w = 1.0 - 1.0 / Math.sqrt(2.0 * Math.PI) * Math.exp(-L * L / 2) * (a1 * K + a2 * K * K + a3

  * Math.pow(K, 3) + a4 * Math.pow(K, 4) + a5 * Math.pow(K, 5))



if (X < 0.0) {

  w = 1.0 - w

}

w

}

}

object OptionSensitivities {

/**

  • Delta of the call option

*/

def deltaCall(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = BlackScholes.d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

math.exp((costOfCarry - discountRate) * timeToExpiry) * BlackScholes.CND(d1)

}

/**

  • Delta of the put option

*/

def deltaPut(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = BlackScholes.d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

math.exp((costOfCarry - discountRate) * timeToExpiry) * (BlackScholes.CND(d1) - 1)

}

/**

  • Elasticity of the call option

*/

def elasticityCall(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

deltaCall(stockPrice, strikePrice, timeToExpiry, discountRate, costOfCarry, volatility) * stockPrice /

  BlackScholes.callOptionGeneralizedBlackScholes(stockPrice, strikePrice, timeToExpiry, discountRate, costOfCarry, volatility)

}

/**

  • Elasticity of the put option

*/

def elasticityPut(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

deltaPut(stockPrice, strikePrice, timeToExpiry, discountRate, costOfCarry, volatility) * stockPrice /

  BlackScholes.putOptionGeneralizedBlackScholes(stockPrice, strikePrice, timeToExpiry, discountRate, costOfCarry, volatility)

}

def nprime(theD: Double) = {

(1 / math.sqrt(2 * math.Pi)) * math.exp(-theD * theD / 2)

}

def vegaCallPut(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = BlackScholes.d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

stockPrice * math.exp((costOfCarry - discountRate) * timeToExpiry) * OptionSensitivities.nprime(d1) * math.sqrt(timeToExpiry)

}

def gammaCallPut(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = BlackScholes.d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

(math.exp((costOfCarry - discountRate) * timeToExpiry) * OptionSensitivities.nprime(d1)) /

  (stockPrice * volatility * math.sqrt(timeToExpiry))

}

def thetaCall(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = BlackScholes.d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

-(stockPrice * math.exp((costOfCarry - discountRate) * timeToExpiry) * nprime(d1) * volatility) / (2 * math.sqrt(timeToExpiry)) -

  (costOfCarry - discountRate) * stockPrice * math.exp((costOfCarry - discountRate) * timeToExpiry) * BlackScholes.CND(d1) -

  discountRate * strikePrice *math.exp(-discountRate*timeToExpiry) * BlackScholes.CND(d2)

}

def thetaPut(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = BlackScholes.d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

-(stockPrice * math.exp((costOfCarry - discountRate) * timeToExpiry) * nprime(d1) * volatility) / (2 * math.sqrt(timeToExpiry)) +

  (costOfCarry - discountRate) * stockPrice * math.exp((costOfCarry - discountRate) * timeToExpiry) * BlackScholes.CND(-d1) +

  discountRate * strikePrice *math.exp(-discountRate*timeToExpiry) * BlackScholes.CND(-d2)

}

def rhoCall(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = BlackScholes.d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

}

def rhoPut(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = BlackScholes.d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

}

def costOfCarrySensitivityCall(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = BlackScholes.d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

}

def costOfCarrySensitivityPut(stockPrice: Double,

strikePrice: Double,

timeToExpiry: Double,

discountRate: Double,

costOfCarry: Double,

volatility: Double) = {

val (d1, d2) = BlackScholes.d1d2(stockPrice, strikePrice, timeToExpiry, costOfCarry, volatility)

}

}

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