Introduction of ELS What is ELSEquityLinked Securities s

Introduction of ELS What is ELS(Equity-Linked Securities)? s ELS is a kind of securities product commercialized in 2003. Which payoff value is decided by the trend of the specific stock price. Its simple principle is as follows. During the specific period(usually for 3 years, ), invested property in ELS is reserved until payoff day. And there are some early payoff days before last payoff day. When stock higher than strike-price(set in specific payoff day), invested property is get refunded with additional coupon interests. Coupon interests get bigger as payoff day got behind. If payoff doesn’t occurred until last payoff day and stock price is lower than strike-price on payoff day, there is two occasionsin ELS, there is a constant knock-in-barrier(Kib) value two separate two occasions. When stock price is below Kib at least one point, investor repay their property at the rate of last day’s stock price. Else, investors repayed their money with additional dummy-interests. (Usually, it’s little bit smaller than last-payoff coupon rate. ) ELS can be seperated by how many stock products are depended on (from one-stock ELS to three-stock ELS. ). Since ELS has a high profitability but high instability, ELS is efficient when small portion of your whole property is invested with lest of your property reserved in a stable market. How can the value of the specific ELS product can be measured? Monte Carlo Simulation Monte Carlo Simuation is process estimating product’s value by modeling correlation between variables in product. By using Monte Carlo Simulation, we can also estimate our ELS’ value my identifying variables in ELS. First, we assume that ELS system follows Geometric Brown-ian Motion(GBM) and Risk-Neutral principle. Then let S(t) be a market price on time t, and б be a variability of market price, and r be a constant zero-risk rate. Then we can get- S(t+Δt)=S(t)exp((r-0. 5 *б^2) Δt+ бsqrt(Δt)Z (Z~N(0, 1)) We can plot S(t) for positive integer t(which used as a day) until repayment day. Then, we can simulate plenty of stock-price path. By applying these in ELS system, we obtain expected value by investing in ELS. 2017160008 Heo Jaeyoung Measuring value with MATLAB clear; r=0. 03; sigma=0. 7; ns=1000; E=100; hold on; %r: risk free rate, sigma: volatility, ns: numbers tried, E: standard price strike_price=[0. 9*E 0. 85*E 0. 8*E]; %strike price at each time Kib=0. 50*E; repay_n=length(strike_price); %kib: knock in barrier, repay_n: the number of redemption date coupon_rate=[0. 02 0. 04 0. 06 0. 08 0. 10 0. 12]; dummy=0. 11; oneyear=360; tot_date=3*oneyear; %dummy rate 0. 11, last maturity redemption after 3 years dt=1/oneyear; S=zeros(tot_date+1, 1); % dt: a day S(1)=100; face_value = 100; % Initial value 100 check_day=ceil(3*oneyear*cumsum(ones(repay_n, 1))/repay_n); % Each check day is at 180*(1, 2, 3, 4, 5, 6) days after tot_payoff=zeros(repay_n, 1); payment=zeros(repay_n, 1); for j=1: repay_n payment(j)=face_value*(1+coupon_rate(j)); end %take 100(1+j’th coupon rate) at j’th redemption for i=1: ns for j=1: tot_date S(j+1)=S(j)*exp((r-0. 5*sigma^2)*dt+sigma*sqrt(dt)*randn); % Monte Carlo Simulation end % made one path: by repeating code, we can get ns paths plot(S) Price_at_check_day=S(check_day+1); payoff(1: repay_n)=0; % initialize the payoff for the new path repay_event=0; for j=1: repay_n if Price_at_check_day(j)>=strike_price(j) payoff(j)=payment(j); % early repayment repay_event=1; %don’t need to check the Kib; this condition is first break %so only first-satisfying row of payoff is nonzero end if repay_event==0 % failed to be repaid early if min(S)>Kib payoff(end)=face_value*(1+dummy); %be repaid (+dummy) if the path never reached under Kib else payoff(end)=face_value*S(end)/E; %If it did, you get paid as the value at the end tot_payoff=tot_payoff+payoff; end tot_payoff=tot_payoff/ns; %average of the total payoff for j=1: repay_n disc_payoff(j)=tot_payoff(j)*exp(-r*check_day(j)/oneyear); %Convert the present value at each redemption point (assume it gains interests r after early-repayment) end ELS_Price = sum(disc_payoff) %expected price of the ELS product (So expected price is measured at last payoff day) ⇒ MATLAB code generating expected value of constructed ELS. Conclusion As we set ns higher, variability of ELS Price gets stable. In this ELS product, expected price is about 95~96 when 100 properties are invested. So stock firm who made this product usually get margin by selling this product. This expected price varies by changing variable’s value( r, sigma, coupon rate, Kib, strike_price, dummy, duration, etc. ) From the standpoint of product-maker, it is important to get appropriate “margin” by adjusting some variables! ⇒ Many cases of Simulated stock-path by MCS.