Pricing American-Options Using the Trinomial Model with Memoization

By Dongliang “Larry” Yi

1. Code

//  main.cpp

//  American_Option_Tri_Memoi

//

//  Created by Dongliang Yi on 11/23/15.

//  Copyright © 2015 Dongliang Yi. All rights reserved.

//

Value-at-Risk Computed Using Various Methods (Historical Simulation, Delta-normal method, Delta-Normal method using the exponentially weighted covariance estimator, Historical simulation using rescaled returns)

By Dongliang “Larry” Yi

Problem:

1.     Historical Simulation

#thousand.000

VaR <- vector("numeric", length=246)

for (i in 1:246)

{

PLGBP = (1000/(data$GBPUSD[i:(i+1999)]*data$UKX[i:(i+1999)]))*data$GBPUSD[(i+1):(i+2000)]*data$UKX[(i+1):(i+2000)]-1000

Key words in “Quantitative Analyst” job postings

By Dongliang “Larry” Yi

Objective: To find most required skills/abilities related to the job of “Quantitative Analyst”

Total Job postings: 13 (Citi, Morgan Stanley, US Bank, Fitch, S&P, Bloomberg, BoA)

Most mentioned skills/abilities:

Programing Skills: 12 times

            C++: specifically mentioned 7 times

Key words in “Risk Analyst” job postings

By Dongliang “Larry” Yi

Objective: To find most required skills/abilities related to the job of “Risk Analyst”

Total number of Job postings: 7 (from Goldman Sachs, Morgan Stanley, US Bank and Citi)

Most mentioned skills/abilities:

Programing Skills: 7 times

            C++: specifically mentioned 4 times

Quantitative Methods for Asian Option Pricing (in C+)

Question:

Below is the analysis report:

Quantitative Methods for Asian Option Pricing

By Dongliang “Larry” Yi

Securities Valuation through NGARCH(1,1), DCC(1,1) and Monte Carlo (in R)

By Dongliang “Larry” Yi

In this article, I used NGARCH(1,1) and DCC(1,1) in correlation and variance prediction of every two indexes’ daily return, then I used Monte Carlo in generating a new daily return. I repeated this process many times and get a prediction of two indexes at Aug. 10^th 2015. The current day is Aug. 5^th 2014.

1.    Securities for pricing

Why we say 1987 Market Crash is caused by derivatives?

By Dongliang “Larry” Yi

Black Monday

On Oct. 19^th, 1987, Dow Jones Industrial Average(DJIA) fell 508.53 points from 2247.27 to 1738.74, which is equal to a 22.61% one-day loss. Until now, it is considered to be the largest one-day percentage decline in the DJIA history^[1][2]. The S&P 500 Index lost 20.5% of its value and the NASDAQ lost 11.3% during the same day^[3].