Reference no: EM132484620
Risk Analysis Assignment Question -
VAR OF A BOND 5 Let us consider a coupon bond with 5 years to maturity, semi-annual coupons, notional coupon at 5% (given on a yearly basis), notional of 100$. The current price of the bond is 105$.
Compute the yield to maturity (ytm), (computation of the ytm has to be done using semi-annual compounding).
Assume that the absolute daily change in the ytm is a Gaussian random variable with mean 0 and daily volatility of 1%: y(t + Δ) - y(t) ∼ N 0%,(1%) 2
(here Δ = 1/250).
Also assume that daily changes in the ytm are i.i.d. random variables.
Compute the probability of losing more than 3% within 10 days.
Compute the VaR99% at 10-days VaR of your bond using
1. Exact formula;
2. Delta approximation (i.e. Taylor's formula arrested to the first order);
3. Monte Carlo with delta-gamma approximation (i.e. Taylor's formula arrested to the second order);
4. Monte Carlo with full revaluation.
Discuss your results. You have to run at least 1,000 Monte Carlo simulations.
Note - Do not need any written essays. Just the excel file or Matlab code or Python code.
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