case : https://www.coursehero.com/file/75161985/Risk-managementpdf/#question

This tutorial attempts to highlight the advantages and limitations of various risk measure methodologies.

Portfolio:

On August 13th 2010 an investor owned the following portfolio:

Long a 1Y forward call on USD against CLP with strike K0 = 450 CLP and a notional of US$1M,

Short a 2Y straddle on USD against CLP with strike K1 = 511.3 CLP and a notional of US$2M,

Short a 4M digital call on USD against CLP with strike K2 = 650 CLP and a notional of US$5M.

Market:

The USD CLP spot on August 13th 2010 was: S0 = 509.61.

For the sake of simplicity, all domestic and foreign interest rates are assumed equal to zero. That is, in the usual Black-Scholes notations: r = q = 0.

Risk:

The USD CLP FX rate is assumed to be the sole source of risk. It is assumed to follow a Geometric Brownian Motion with drift = 0.0264 and volatility = 0.0819.

The homework considers only market risk.

Model:

All pricing formulae derive from Black-Scholes in this homework.

Question 1:

Compute the current value of the portfolio.

Question 2:

Sensitivities: What is the sensitivity of the portfolio value with respect to the FX rate? Which product has the largest delta (in absolute value)? Which one has the smallest delta (in absolute value)?

Question 3:

Linear Value at Risk: The aforementioned drift and volatility estimates for the FX rate correspond are based on historical data. Compute the 99% 1 day linear parametric Value at Risk.

Question 4:

Parametric Value at Risk: Using the Black-Scholes model, simulate 1,000 FX rates with a 1 day horizon and estimate the 99% 1 day parametric Value at Risk, as well as the maximum tension. How does this estimate compare to the linear VaR? Why is the result different?

Question 5:

Value at Risk decomposition: Compute the incremental, marginal, and component Value at Risk of the straddle.

Question 6:

Stress test: Dramatic news affected the United States of America and the CLP suddenly jumps to 700CLP/USD. Compute the corresponding P&L.

Question 7:

Summarize the results of the previous questions and make recommendations to the investor.

Hello

1. How do I find the correct answer to question 2? It gives me -6405983 which I am not sure and I would like to check
2. How do I find the correct answer to question 4? It gives me -6566155.412, I'm not sure it's correct
3. How do I find the correct answer to question 6?