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 Evaluation report: Quant consultant

John Lewis
 Candidate Session ID : 56 Mail : hh820731@gmail.com Phone : Degree : Msc Quantitative Finance School/University : Imperial college Experience : 1 Your comment : Candidate comment: . ID session : c4kg Started : 2017-05-02 21:42:09 Finished : 2017-05-02 22:28:41

Test Test type Absolute score Relative score
1. Quantitative Finance MCQ 3 / 6
50%
2. [C++] VAR ,Expected shortfall Coding 5 / 5
76%
3. [C++] Implied volatility Coding 5 / 5
85%
Global score

13 / 16
.
1. Quantitative Finance

1-1. Details MCQ

Question 1 "Consider 3 Call options of the same maturity T and with different strikes K1=10, K2=20 and K3=30.If we buy today one call with strike K3 and one with strike K1 and sell two call options with the strike K2, should this cost us money or should we paid for that ? ": Yes, this must cost us money. Yes, this must cost us money. 1
Question 2 "Compute where W is a Brownian motion and ? is the volatility. Select the from the following: ": c c 1
Question 3 "Compute the following covariance for 0 <s <t, select the right answer from the following: ": b a 0
Question 4 "Compute the following covariance for 0 < s < t: Select the right answer from the following: ": c c 1
Question 5 "Compute the following integral for a given x : Select the right answer from the following: ": a c 0
Question 6 "Suppose X is a random variable with : What is the constant C that minimizes: Select the right answer from the following: ": d a 0

2. [C++] VAR ,Expected shortfall
2-1. Subject coding

VaR computation test

1- Description:
This test consists on computing the VaR of a portfolio with the historical method. Given the historical daily PnL of the given portfolio, the objective is to compute the Value at Risk for a given level of confidence(95% for example). A skeleton of the code is provided. .

2- Objective:
The objective is to implement the method var(...) that returns the VaR given the history of daily PnLs at a given confidence level(95% for example).

3- Provided code:
You only need to implement the var method. 4- Important remarks:
- In its final version, your code should not print anything to the console.You can print values only for debugging purpose. Please make sure that you remove any printing instructions before submitting your final version.

- Press the button Execute to launch a unit test of your solution.

 Language : cpp    Compilation:Successfully   Marks Scored: 5/5
2-2. Unit test cases

Test name Candidate Output Value Correct output Execution time Memory consumption Result
Unit test1-3.794 -3.794 0.00 sec0 KB Passed
Unit test2-2.35674 -2.35674 0.00 sec0 KB Passed
Unit test3-1.60828 -1.60828 0.00 sec0 KB Passed
Unit test4-1.24225 -1.24225 0.00 sec0 KB Passed
Unit test5-0.811638 -0.811638 0.00 sec0 KB Passed

2-3. Candidate Source code

Main File: Risk.h

```// Histirical VAR

#include <iostream>
#include <iomanip>
#include <vector>
#include <math.h>
#include <stdlib.h>
#include <time.h>
#include <algorithm>

using namespace std;

//VAR compute the historical VAR for one day for the portfolio with Pnl as daily pnl vector
// pnl is the daily pnl vector
// threshold is the var thresold ex 0.95

double var(vector<double> pnl,double threshold) {

std::sort(pnl.begin(),pnl.end());
size_t SizeSample = pnl.size();
double rank_min = floor((1-threshold)*SizeSample);
return pnl.at(rank_min);

return 0 ;
}```

3. [C++] Implied volatility
3-1. Subject coding

Black Scholes Implied vol [C++]

1- Description:
This test consists of creating a European option implied volatility, under the Black-Scholes model (extended for dividends by Merton). A skeleton of this implied volatility tool is provided.

2- Objective:
The objective of this test is to Implement the following function BSImpliedVol (...) to return the implied volatility of the option (a function BS (...) giving the price by the closed formula is provided to help you).

3- The skeleton code provided:
NormalFunctions.h // Math / utility function
Volatility.h // the file BSImpliedVol based implied vol

4- Note:
1- the only work to do is to complete the implementation of the BSImpliedVol function (...) File Volatility.h

2-Your code does not print the screen unless you want to test / debuger in this case make sure you remove these impressions screen before submitting your solution

3- The run button allows you to run a unit test on your solution

 Language : cpp    Compilation:Successfully   Marks Scored: 5/5
3-2. Unit test cases

Test name Candidate Output Value Correct output Execution time Memory consumption Result
Unit test10.25 0.25 0.00 sec0 KB Passed
Unit test20.25 0.25 0.00 sec0 KB Passed
Unit test30.25 0.25 0.00 sec0 KB Passed
Unit test40.250154 0.25 0.00 sec0 KB Passed
Unit test50.449998 0.45 0.00 sec0 KB Passed

3-3. Candidate Source code

Main File: Volatility.h

```// Implied volatility  Black-Scholes

#include <iostream>
#include <iomanip>
#include <vector>
#include <math.h>
#include <stdlib.h>
#include <time.h>
#include <algorithm>
#include "NormalFunctions.h"
using namespace std;

//BSImpliedVol compute the implied volatility of an european option using Black Scholes model
// S Spot Price
// optPrice market option Price
// v Volatility
// T Maturity in Years
// rf Interest Rate
// q Dividend  yeild
// PutCall 'P' for put and 'C' for call
// Nsims Number of simulations

double BSImpliedVol(double S,double K,double optPrice,double T,double rf,double q,char PutCall) {

size_t N = 40;
size_t i(0);
double x = 0.;
double y = 1.;
double z = 0.;
double sigma = 0.;

if(PutCall == 'C')
{
for(; i < N; ++i)
{
z = 0.5*(x+y);
double temp_v = z/(1-z);
if(optPrice > BS(S,K,temp_v,T,rf,q,'C'))
{
x = z;
}
else
{
y = z;
}
}

z = 0.5*(x+y);
sigma = z/(1-z);
}
else if(PutCall == 'P')
{
for(; i < N; ++i)
{
z = 0.5*(x+y);
double temp_v = z/(1-z);
if(optPrice > BS(S,K,temp_v,T,rf,q,'P'))
{
x = z;
}
else
{
y = z;
}
}

z = 0.5*(x+y);
sigma = z/(1-z);
}

return sigma;
}```