代做Exercise-3: Monte Carlo Method Implementation to Price a Derivative Product代写留学生Matlab语言程序

日期：2025-11-07 05:57

Exercise-3: Monte Carlo Method Implementation to Price a Derivative Product

Description of the Structured Product:

Reverse Convertible Bond
Issuer	XYZ
Maturity (T)	1 month (1/12 year)
Notional Amount (N)	$1,000
Issue Price	N x (100% - X), where X is the ''Discount''
Underlying share (St)	a listed stock
Initial share price (S0)	the share price at the product trade date (and time)
Strike (K)	95%
Final Redemption at Maturity	At maturity, the investor will receive: - in cash, if ST/S0; > = K; - shares where KxS0/N, otherwise.

Stock and Model related Parameters:

- Initial stock price: S0 = $100

- Black-Scholes-Merton risk-neutral model: dSt/St = rdt + σ dWt

- “risk-free” interest rate: r = 3.5% p.a.

- volatility of St: σ = 30%

- Total margin for the issuer: 0.30% x N

Product Return Illustration:

Assume that

- Discount X = 1%

- Final share price ST = $96

The initial investment of the investor is

N x (100% - 1%) = $990

At maturity, the final redemption for the investor will depend on the final share price (ST):

Scenario	Final share price ST	Condition test	Final redemption for the investor
1	96	96/100 > 95%	Investor will receive cash of $1,000
2	90	90/100 < 95%	Investor will receive shares instead of cash; the number of shares is $1000/(95% x $100) = 10.52

Implementation Requirement:

Use Excel sheet and Monte Carlo method with 5000 paths (spreadsheet or VBA at your choice) for the below three items:

1) (9 points) X = ? (precision 0.01%)

2) (2 points) Draw the graphical representation of the possible values of the final redemption (ST range $5 - $115 with step of $10)

3) (2 points) Draw the graphical representation of the possible mark-to-market prices of the product with the time to maturity of 1/2 month (St range: $5 - $150 with step of $10)

4) (2 points) For hedging the market risk from share price changes, what is the quantity of shares that the issuer needs to hold at the inception of the product? Is it a short or a long position for the shares to hold?

Submission Requirement:

Materials to submit: your Excel sheet with the answers embedded

Note:

In Excel, the useful functions for the project are

1) u = RAND() for generating a uniformly distributed rand number between 0 and 1;

2) g = NORMSINV(u) for generating a standard normal variate from a uniformly distributed random between 0 and 1.

Exercise-4: Binomial Tree Method Implementation to Price a Derivative Product

(5 points) Build a 5-period binomial tree with Excel for pricing a 5-month (5/12 year) American Call option linked to a stock under BSM model.

· The option strike is $10 and the initial stock price is $10.

· The dividend yield and stock lending rate are all zero.

· The interest rate is 2.5% and the volatility of the stock is 22%.