Valuing an equity option using the simple Black-Scholes Model

This example illustrates pricing of vanilla options using a constant volatility Black-Scholes Model. The process of pricing the option consists of three logical steps:

1. Creating a description of the process governing the price of the underlying. In this case this is done using functions qlGeneralizedBlackScholesProcess and qlBlackConstantVol. The interest rates is defined by single values for the risk-free rate and the dividend yield (dividends are assumed to be continuous)

2. Create a description of the option to price. This is done by combination of calls to qlEuropeanExercise, qlStrikedTypePayoff and qlVanillaOption

3. Create a pricing engine and assign it to be used for pricing the derivative

The example prices a call option with strike at 110 and exercise date on 1st June 2012. The volatility is specified to be 0.25, today’s date is 1st June 2011, the interest free rate is assumed to be 5% and the dividend yield is 2%.

today’s date	2011-06-01	->	today’s date	2011-06-01
set global evaluation date	=qlSettingsSetEvaluationDate(R[-1]C)	->	set global evaluation date	nil
settlement date	=R[-2]C+2	->	settlement date	2011-06-03
calendar	TARGET	->	calendar	TARGET
volatility	0.25	->	volatility	0.25
day counter	Actual/365 (Fixed)	->	day counter	Actual/365 (Fixed)
black constant vol object	=qlBlackConstantVol(“blackvol1”,R[-4]C,R[-3]C,R[-2]C,R[-1]C)	->	black constant vol object	blackvol1#0009
underlying	100	->	underlying	100
risk free rate	0.05	->	risk free rate	0.05
dividend yield	0.02	->	dividend yield	0.02
stochastic process object	=qlGeneralizedBlackScholesProcess(“blackscholes1”,R[-4]C,R[-3]C,R[-5]C,R[-8]C,R[-2]C,R[-1]C)	->	stochastic process object	blackscholes1#0016
exercise date	2012-06-01	->	exercise date	2012-06-01
exercise object	=qlEuropeanExercise(“eu_exercise2”,R[-1]C)	->	exercise object	eu_exercise2#0005
payoff type	Vanilla	->	payoff type	Vanilla
option type	CALL	->	option type	CALL
strike	110	->	strike	110
striked type payoff	=qlStrikedTypePayoff(“eu_payoff”,R[-3]C,R[-2]C,R[-1]C)	->	striked type payoff	eu_payoff#0007
pricing engine	=qlPricingEngine(“eur_example_engine”,”AE”,R[-7]C)	->	pricing engine	eur_example_engine#0017
european option	=qlVanillaOption(“european_option”,R[-2]C,R[-6]C)	->	european option	european_option#0012
set engine	=qlInstrumentSetPricingEngine(R[-1]C,R[-2]C)	->	set engine	nil
NPV	=qlInstrumentNPV(R[-2]C,R[-1]C)	->	NPV	7.10

Here is the same example in QLW – QuantLib-Addin like interface from Java and Python

// Copyright (C) 2012 Bojan Nikolic <bojan@bnikolic.co.uk>
//

import co.uk.bnikolic.qlw.property_t;
import co.uk.bnikolic.qlw.qlw;
import co.uk.bnikolic.qlw.StringVector;
import co.uk.bnikolic.qlw.LongVector;
import co.uk.bnikolic.qlw.PropertyVector;

public class BlackScholesSimple {

    public static void main(String[] args) throws Exception {

        property_t today=new property_t(40695);
        
        property_t settlementdate=new property_t(40697);
        property_t excersisedate=new property_t(41061);

        property_t dcc=new property_t("Actual/365 (Fixed)");

        qlw.qlSettingsSetEvaluationDate(today);

        String payoff=qlw.qlStrikedTypePayoff("payoff", 
                                              "Vanilla", 
                                              "Call", 
                                              110.0,
                                              qlw.OH_NULL()
                                              );

        String exercise=qlw.qlEuropeanExercise("exercise", 
                                               excersisedate);

        String option=qlw.qlVanillaOption("option",
                                          payoff, 
                                          exercise);


        String vol=qlw.qlBlackConstantVol("vol",
                                          settlementdate, 
                                          "TARGET", 
                                          0.25, 
                                          dcc);

        String process=qlw.qlGeneralizedBlackScholesProcess("process", 
                                                            "vol",
                                                            100.0, 
                                                            dcc,
                                                            settlementdate, 
                                                            0.05, 
                                                            0.02)        ;

        String pengine=qlw.qlPricingEngine("pengine", 
                                           "AE",
                                           process);

        qlw.qlInstrumentSetPricingEngine(option, pengine);

        System.out.println("NPV: "+ qlw.qlInstrumentNPV(option));
        
                

    }

}