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

The securities do not guarantee the repayment of any principal. The securities will pay a fixed monthly coupon (including at maturity) at the rate specified below. At maturity, if the final share price of each of the iShares® Russell 2000® ETF and the iShares® MSCI EAFE ETF, which we refer to as the underlying shares, is greater than or equal to 85% of its respective initial share price, meaning that neither of the underlying shares has declined by an amount greater than the buffer amount of 15%, investors will receive the stated principal amount of the securities. However, if the final share price of either of the underlying shares is less than 85% of its initial share price, meaning that either of the underlying shares has declined by an amount greater than the buffer amount of 15%, investors will lose 1.1765% of the principal amount for every 1% decline in the final share price of the worst performing underlying shares from its initial share price beyond the buffer amount of 15%.                                                                      

2.    Historical data used for prediction

The underlying assets’ data is from Yahoo finance. The data is “adjusted close index” from Jan. 2^nd, 2009 to Aug. 5^th, 2014.

3.    NGARCH

The two NGARCH model is derived by MLE as follows:

4.    DCC

The DCC model is as follows:

5.    Monte Carlo

We used 5000 trials for Monte Carlo, and kept updating:

with generating two correlated normal RVs (Return). Each payoff needs 255 steps which corresponds to the working days until Aug. 10^th 2015.

6.    Result

The simulated price of this asset is at Aug. 5^th 2014:

Please be noted that we used 12 month historical(2014) Libor for discounting cash flows of this asset.