C++ 혹은 Excel/VBA로 배우는 투자금융

1.
Best Programming Languages for Finance & FinTech in 2022을 보면 금융에서 가장 많이 필요로 하는 언어를 순서대로 정리하고 있습니다. 예상대로 Python의 순위가 가장 높네요. 데이타, 기계학습하면 떠오르는 언어이기 때문입니다.또다른 Best Programming Languages for Finance & Fintech in 2022을 보더라도 역시나 Python이 높습니다. 그 기사를 비교해서 보면 가장 큰 차이점은 Scala입니다. 나라마다 환경이 다르니까 순위도 차이가 있는 듯 합니다. 저와 같은 또래들이 가장 많이 사용하였던 C/C++의 순위는 떨어지지 않지만 그렇다고 오르지도 않습니다. 생산성과 CI/CD 및 애자일이 중요한 문화에서 C++의 지위가 높아지기 힘들어 보입니다. 그럼에도 불구하고 여러가지 이유로 – 가장 중요한 점은 속도 – C++을 배우고자 하는 사람, 그 중에서 금융실뭉에 적용해보고자 하는 사람을 위한 책입니다.

Financial analysis and investment using language programming C++

저자는 유명한 분은 아닙니다. Michel Guirguis인데 그리스 분입니다. SSRN에 올라온 논문을 보면 주로 실용적인 논문으로 암호통화, 헤지펀드와 관련한 내용을 다루고 있습니다. 위 논문을 보면 금융회사에 다니는 사람이 C++를 이용하여 금융실무를 할 수 있도록 안내합니다. 예를 소개합니다. Calculation of portfolio variance and standard deviation을 다루고자 합니다.

위 과제를 C++로 어떻게 구현할까요? 위 책은 아래와 같이 보여줍니다.

// Calculation of portfolio variance and standard deviation.
#include <iostream>
#include<cmath>
using namespace std;
int main()
{
//Identify the variables.
double WeightShare = 0.80;
double StandardDeviationShare = 0.20;
double WeightSilver= 0.20;
double StandardDeviationSilver = 0.12;
double Variance;
double StandardDeviationPercentage;
/* Insert the mathematical formulas.As correlation is zero, we do not include the last
part of the equation.*/
Variance =pow(WeightShare*StandardDeviationShare,2)+
pow(WeightSilver*StandardDeviationSilver,2) ;
StandardDeviationPercentage = sqrt(Variance)*100;
// Output functions.
209
Electronic copy available at: https://ssrn.com/abstract=3854475cout<< " Variance :"<< Variance <<endl;
cout<< " Standard deviation Percentage :"<< StandardDeviationPercentage <<endl;
system ("PAUSE");
return 0;
}

// Calculation of portfolio variance and standard deviation.

#include <iostream>

#include<cmath>

using namespace std;

int main()

{

//Identify the variables.

double WeightShare = 0.80;

double StandardDeviationShare = 0.20;

double WeightSilver= 0.20;

double StandardDeviationSilver = 0.12;

double Variance;

double StandardDeviationPercentage;

/* Insert the mathematical formulas.As correlation is zero, we do not include the last

part of the equation.*/

Variance =pow(WeightShare*StandardDeviationShare,2)+

pow(WeightSilver*StandardDeviationSilver,2) ;

StandardDeviationPercentage = sqrt(Variance)*100;

// Output functions.

209

Electronic copy available at: https://ssrn.com/abstract=3854475cout<< " Variance :"<< Variance <<endl;

cout<< " Standard deviation Percentage :"<< StandardDeviationPercentage <<endl;

system ("PAUSE");

return 0;

}

또다른 예입니다. Compare the call option price using a Jarrow – Rudd, (JR), binomial 3 steps tree with the Black and Scholes model입니다.

/* Calculate the call option prices using a Cox, Ross, Rubinstein,(CRR)
binomial 3 steps tree. */
#include <iostream>
#include<cmath>
using namespace std;
int main()
{
double S = 60;
double K = 50;
double r = 0.05;
double q = 0.02;
double T = 0.5;
double sig = 0.3;
//share price
// strike price
// risk-free interest rate
// dividend yield. If the dividend is zero, then, it is
// not included in the equation of risk neutral
// probability of upmove.
// life to maturity
// volatility
// Identify the variables.
// u = multiplier of upmove.
//d = multiplier of downmove. dt = steps expressed in years.
//riskprobofupmove = risk neutral probability of upmove.
//disfact = discount factor.
double u;
double d;
double dt;
double riskprobofupmove;
double disfact;
const int n = 3; // Identify tree steps binomial tree.
// Insert the mathematical formulas.
dt = T/n;
u = exp(sig*sqrt(dt));
d = 1/u;
disfact = exp(-r*dt);
riskprobofupmove = (exp((r-q)*dt)-d)/(u-d);
double callpayoffupmovestep3; // (Shareprice * upmove^3)-K
double callpayoff3i;
// (Shareprice * upmove^2 * downmove)-K
double callpayoff3ii;
// (Shareprice * downmove^2*upmove)-K
Electronic copy available at: https://ssrn.com/abstract=3854475double callpayoffdownmovestep3; // (Shareprice * downmove^3) -K
// The option prices are calculated backwards.
callpayoffupmovestep3 = S*pow(u,3)-K;
callpayoff3i = S * pow(u,2) * d -K;
callpayoff3ii =S * pow(d,2)*u-K;
callpayoffdownmovestep3 = S*pow(d,3)-K;
callpayoffdownmovestep3 =0;
double callpriceupmovestep2;
double callpriceupdownmovestep2;
double callpricedownmovestep2;
callpriceupmovestep2 = (disfact*(riskprobofupmove*callpayoffupmovestep3)
+(1-riskprobofupmove)*callpayoff3i);
callpriceupdownmovestep2 =(disfact*(riskprobofupmove*callpayoff3i)
+(1-riskprobofupmove)*callpayoff3ii);
callpricedownmovestep2 =(disfact*(riskprobofupmove*callpayoff3ii)
+(1-riskprobofupmove)*callpayoffdownmovestep3);
double callpriceupmovestep1;
double callpricedownmovestep1;
callpriceupmovestep1 = (disfact*(riskprobofupmove*callpriceupmovestep2)
+(1-riskprobofupmove)*callpriceupdownmovestep2);
callpricedownmovestep1=(disfact*(riskprobofupmove*callpriceupdownmovestep2)
+(1-riskprobofupmove)*callpricedownmovestep2);
double callpricestep0;
callpricestep0= (disfact*(riskprobofupmove*callpriceupmovestep1)
+(1-riskprobofupmove)*callpricedownmovestep1);
//Output functions.
cout.setf(ios::fixed);
cout.setf(ios::showpoint);
cout.precision(4);
cout<<"Steps expressed in years:"<< dt<<endl;
cout<<"Multiplier of upmove:"<< u<<endl;
cout<<"Multiplier of downmove:"<< d<<endl;
cout<<" Discount factor:"<<disfact<<endl;
cout<< "Risk neutral probability of upmove:"<<riskprobofupmove<<endl;
cout<<"Call payoff upmove step [3]:"<<callpayoffupmovestep3<<endl;
cout<<"Call payoff [3i]:"<<callpayoff3i<<endl;
Electronic copy available at: https://ssrn.com/abstract=3854475cout<<"Call payoff [3ii]:"<<callpayoff3ii<<endl;
cout<<"Call payoff downmove step [3]:"<<callpayoffdownmovestep3<<endl;
cout<<"Call price upmove step[2]:"<<callpriceupmovestep2<<endl;
cout<<"Call price updownmove step [2]:"<<callpriceupdownmovestep2<<endl;
cout<<"Call price downmove step [2]:"<<callpricedownmovestep2<<endl;
cout<<"Call price upmove step [1]:"<<callpriceupmovestep1<<endl;
cout<<"Call price downmove step [1]:"<<callpricedownmovestep1<<endl;
cout<<"Call price step[0]:"<<callpricestep0<<endl;
system ("PAUSE");
return 0;
}

/* Calculate the call option prices using a Cox, Ross, Rubinstein,(CRR)

binomial 3 steps tree. */

#include <iostream>

#include<cmath>

using namespace std;

int main()

{

double S = 60;

double K = 50;

double r = 0.05;

double q = 0.02;

double T = 0.5;

double sig = 0.3;

//share price

// strike price

// risk-free interest rate

// dividend yield. If the dividend is zero, then, it is

// not included in the equation of risk neutral

// probability of upmove.

// life to maturity

// volatility

// Identify the variables.

// u = multiplier of upmove.

//d = multiplier of downmove. dt = steps expressed in years.

//riskprobofupmove = risk neutral probability of upmove.

//disfact = discount factor.

double u;

double d;

double dt;

double riskprobofupmove;

double disfact;

const int n = 3; // Identify tree steps binomial tree.

// Insert the mathematical formulas.

dt = T/n;

u = exp(sig*sqrt(dt));

d = 1/u;

disfact = exp(-r*dt);

riskprobofupmove = (exp((r-q)*dt)-d)/(u-d);

double callpayoffupmovestep3; // (Shareprice * upmove^3)-K

double callpayoff3i;

// (Shareprice * upmove^2 * downmove)-K

double callpayoff3ii;

// (Shareprice * downmove^2*upmove)-K

Electronic copy available at: https://ssrn.com/abstract=3854475double callpayoffdownmovestep3; // (Shareprice * downmove^3) -K

// The option prices are calculated backwards.

callpayoffupmovestep3 = S*pow(u,3)-K;

callpayoff3i = S * pow(u,2) * d -K;

callpayoff3ii =S * pow(d,2)*u-K;

callpayoffdownmovestep3 = S*pow(d,3)-K;

callpayoffdownmovestep3 =0;

double callpriceupmovestep2;

double callpriceupdownmovestep2;

double callpricedownmovestep2;

callpriceupmovestep2 = (disfact*(riskprobofupmove*callpayoffupmovestep3)

+(1-riskprobofupmove)*callpayoff3i);

callpriceupdownmovestep2 =(disfact*(riskprobofupmove*callpayoff3i)

+(1-riskprobofupmove)*callpayoff3ii);

callpricedownmovestep2 =(disfact*(riskprobofupmove*callpayoff3ii)

+(1-riskprobofupmove)*callpayoffdownmovestep3);

double callpriceupmovestep1;

double callpricedownmovestep1;

callpriceupmovestep1 = (disfact*(riskprobofupmove*callpriceupmovestep2)

+(1-riskprobofupmove)*callpriceupdownmovestep2);

callpricedownmovestep1=(disfact*(riskprobofupmove*callpriceupdownmovestep2)

+(1-riskprobofupmove)*callpricedownmovestep2);

double callpricestep0;

callpricestep0= (disfact*(riskprobofupmove*callpriceupmovestep1)

+(1-riskprobofupmove)*callpricedownmovestep1);

//Output functions.

cout.setf(ios::fixed);

cout.setf(ios::showpoint);

cout.precision(4);

cout<<"Steps expressed in years:"<< dt<<endl;

cout<<"Multiplier of upmove:"<< u<<endl;

cout<<"Multiplier of downmove:"<< d<<endl;

cout<<" Discount factor:"<<disfact<<endl;

cout<< "Risk neutral probability of upmove:"<<riskprobofupmove<<endl;

cout<<"Call payoff upmove step [3]:"<<callpayoffupmovestep3<<endl;

cout<<"Call payoff [3i]:"<<callpayoff3i<<endl;

Electronic copy available at: https://ssrn.com/abstract=3854475cout<<"Call payoff [3ii]:"<<callpayoff3ii<<endl;

cout<<"Call payoff downmove step [3]:"<<callpayoffdownmovestep3<<endl;

cout<<"Call price upmove step[2]:"<<callpriceupmovestep2<<endl;

cout<<"Call price updownmove step [2]:"<<callpriceupdownmovestep2<<endl;

cout<<"Call price downmove step [2]:"<<callpricedownmovestep2<<endl;

cout<<"Call price upmove step [1]:"<<callpriceupmovestep1<<endl;

cout<<"Call price downmove step [1]:"<<callpricedownmovestep1<<endl;

cout<<"Call price step[0]:"<<callpricestep0<<endl;

system ("PAUSE");

return 0;

}

226쪽을 이런 식으로 구성하였습니다. 궁금한 점이 있으면 이메일로 질문을 하라고 합니다.

Download (PDF, 1.2MB)

2.
저자가 위 논문에서 추천하는 책이 있습니다. Chandan Sengupta가 쓴 Financial Modeling using C++ 입니다. 자료를 구해서 대략 살펴보니까 눈에 들어오는 부분이 Review of Theory and Concepts라는 부분입니다. Time Value Of Money를 주제한 부분에서 개념을 길게 설명합니다. 투자와 금융에서 “시간이 왜 중요한지”를 소개합니다. 그리고 이런 개념에 기반하여 Mdeling Examples을 다룹니다. 구글링을 하시면 찾아보실 수 있습니다. 이 분의 또다른 저작인 Financial Modeling Using Excel and VBA도 확인하니까 비슷한 구성입니다. 개념과 예제르 이루졌네요. Excel과 관련한 자료는 Financial Modeling Using Excel and VBA에서 받을 수 있습니다.

Part Four: Financial Modeling Using VBA.

CHAPTER 18: How to Build Good VBA Models.
CHAPTER 19: Time Value of Money.
CHAPTER 20: Financial Planning and Investments.
CHAPTER 21: Analyzing Market History.
CHAPTER 22: Simulating Stock Prices.
CHAPTER 23: Options and Option Portfolios.
CHAPTER 24: Binomial Option Pricing.

투자금융을 하시는 분들의 경우 C++이든 Excel이든 업무에 도움을 받을 수 있을 듯 합니다.

C++ 혹은 Excel/VBA로 배우는 투자금융

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