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Re: BLS IV calculated by QuantLib is different from Hull's

Posted by animesh on
URL: http://quantlib.414.s1.nabble.com/BLS-IV-calculated-by-QuantLib-is-different-from-Hull-s-tp213p214.html

Hi,
   In your calcuation and Hull White there is difference of 7%. There is no formula for calculating implied vol accurately. What traders/quants generally do is put an implied volatility in option pricing formula to price the option. If it matches the market price then you have the implied volatility.

For example Call Price = S N(d1) - K e^-(rT) N(d2)
d1 and d2 are again standard definitions d1 = (Log(S/K) + (r + sigma^2/2)(T))/(sigma (T)^0.5)
d2 = d1 - sigma (T)^0.5

What I would suggest is use the different volatilities in the range (0.60 - 0.80) to price the Put option and see which one is closest to the price you want.
You can do the same thing online if you want a rough check here.....
http://www.sitmo.com/live/OptionVanilla.html

Also am not sure if time is being calculated by Number of Days / 365 or Number of Days / 252.


On 9/6/10 9:46 PM, Alex Cicco wrote:
Hi All,

I am new to quant lib.  So, please forgive my newbie question. 

My System Quantlib + boost + Java Swig interface. 
I am using a Java testing code adapted from the work by  Richard Gomes and Tito Ingargiola on Equity Options.
The testing code is enclosed at the end of this email.

My trouble is:
I cannot get BLS European IV calculated by QuantLib tied out with the value generated by Hull's DerivativeGem

------------------------------------------------------------------------------------------------------------------------------
Here is my input for the computation of an equity option IV

Trading Date: 2008-12-01,
Underlying stock price: 55.08,
Option Strike: 42.5,
Option Type: Put
Option Price: 0.215,
riskFreeRate = 0.03;
dividendYield = 0.00;
Option Expiration Date: 2008-12-20 ( the Saturday following the third Friday of the month)
--> Option Time to Expiration: 15 days  (when counting trading days, I include 12/01/2008 as the option trading takes place at 9:30 of 12/01/2008)

--------------------------------------------------------------------------------------------------------------------------------------
Using the above input, and Hull's DerivativeGem Excel worksheet, I got an IV of 0.6897

-----------------------------------------------
Using QuantLib, I set

Try 1:
TodaysDate = 12/01/2008
SettlementDate =12/01/2008,
Maturity Date = 12/20/2008.
I got an IV of 0.7398648108461248

Try 2:
TodaysDate = 12/01/2008
SettlementDate =12/03/2008,
Maturity Date = 12/20/2008.
I got an IV of 0.7817627320081257
------------------------------------------------------------------------------------------------------------------------------------------------------

Could you advise on which parameter I set wrong in using QuantLib?

Thank you very much

Best regards,

Alex
------------------------------------------------------------------------------------------------------------------------------------------------------

My Java Testing Code goes here

package com.alexCicco.test.quantLibTest;


/*
 Copyright (C) 2007 Richard Gomes
 Copyright (C) 2007 Tito Ingargiola

 This file is part of QuantLib, a free-software/open-source library
 for financial quantitative analysts and developers - http://quantlib.org/

 QuantLib is free software: you can redistribute it and/or modify it
 under the terms of the QuantLib license.  You should have received a
 copy of the license along with this program; if not, please email
 <[hidden email]>. The license is also available online at
 <http://quantlib.org/license.shtml>.

 This program is distributed in the hope that it will be useful, but WITHOUT
 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 FOR A PARTICULAR PURPOSE.  See the license for more details.
*/

//package examples;

import org.quantlib.Actual365Fixed;
import org.quantlib.AmericanExercise;

import org.quantlib.BlackConstantVol;
import org.quantlib.BlackScholesMertonProcess;

import org.quantlib.AnalyticEuropeanEngine;
import org.quantlib.BlackVolTermStructureHandle;
import org.quantlib.Calendar;
import org.quantlib.Date;

import org.quantlib.DayCounter;
import org.quantlib.EuropeanExercise;
import org.quantlib.Exercise;

import org.quantlib.FlatForward;

import org.quantlib.Month;
import org.quantlib.Option;
import org.quantlib.Payoff;

import org.quantlib.PlainVanillaPayoff;

import org.quantlib.QuoteHandle;
import org.quantlib.Settings;
import org.quantlib.SimpleQuote;

import org.quantlib.TARGET;

import org.quantlib.VanillaOption;

import org.quantlib.YieldTermStructureHandle;

/**
 * Test Implied volatility of European options
 * @author Alex Cicco
 */
public class EuropeanIV {

    static {
        try {
            System.loadLibrary("QuantLibJNI");
        } catch (RuntimeException e) {
            e.printStackTrace();
        }
    }

    public static void main(String[] args) throws Exception {
       
        long beginTime = System.currentTimeMillis();

        // our option
        Option.Type type = Option.Type.Put;
        double strike = 42.5;
        double underlying = 55.08;
        double riskFreeRate = 0.03;
        double dividendYield = 0.00;
        double volatility = 0.01;
       
        Date todaysDate = new Date(1, Month.December, 2008);
        Date settlementDate = new Date(1, Month.December, 2008);
        Settings.instance().setEvaluationDate(todaysDate);
               
        Date maturity = new Date(20, Month.December, 2008);
        DayCounter dayCounter = new Actual365Fixed();
        Calendar calendar = new TARGET();

        Exercise europeanExercise = new EuropeanExercise(maturity);
        Exercise americanExercise = new AmericanExercise(settlementDate, maturity);
 
        // define the underlying asset and the yield/dividend/volatility curves
        QuoteHandle underlyingH = new QuoteHandle(new SimpleQuote(underlying));
       
        YieldTermStructureHandle flatTermStructure =
            new YieldTermStructureHandle(new FlatForward(
                                  settlementDate, riskFreeRate, dayCounter));
       
        YieldTermStructureHandle flatDividendYield =
            new YieldTermStructureHandle(new FlatForward(
                                  settlementDate, dividendYield, dayCounter));
       
        BlackVolTermStructureHandle flatVolatility =
            new BlackVolTermStructureHandle(new BlackConstantVol(
                           settlementDate, calendar, volatility, dayCounter));

        BlackScholesMertonProcess stochasticProcess =
            new BlackScholesMertonProcess(underlyingH,
                                          flatDividendYield,
                                          flatTermStructure,
                                          flatVolatility);

        // options
        Payoff payoff = new PlainVanillaPayoff(type, strike);

        VanillaOption europeanOption =
            new VanillaOption(payoff, europeanExercise);
       
        VanillaOption americanOption =
            new VanillaOption(payoff, americanExercise);

        double optionPrice = 0.215;
       
        europeanOption.setPricingEngine(
                new AnalyticEuropeanEngine(stochasticProcess));
       
        double iv_european = europeanOption.impliedVolatility(optionPrice, stochasticProcess);
       
       
        double iv_american = americanOption.impliedVolatility(optionPrice, stochasticProcess);
       
        String fmt = "\n%-35s %-35s %-35s\n";
        System.out.printf(fmt, "Method", "European_IV", "American_IV");
        System.out.println("=====================================================================================");
       
        // Black-Scholes for European
        String method = "Black-Scholes";
        System.out.printf(fmt, new Object[] { method,
                                              iv_european,                                             
                                              Double.NaN } );      

        // Bjerksund and Stensland approximation for American
        method = "American: Bjerksund/Stensland";       
        System.out.printf(fmt, new Object[] { method,
                                              Double.NaN,
                                              iv_american } );

        long msecs = (System.currentTimeMillis()-beginTime);
        System.out.println("Run completed in "+msecs+" ms.");

    }
}



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-- 
Regards,
Animesh Saxena

(http://quantanalysis.wordpress.com)
Ph: (+91)9920098221

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