Exercise-3: Monte Carlo Method Implementation to Price a Derivative Product
Description of the Structured Product:
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Reverse Convertible Bond
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Issuer
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XYZ
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Maturity (T)
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1 month (1/12 year)
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Notional Amount (N)
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$1,000
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Issue Price
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N x (100% - X), where X is the ''Discount''
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Underlying share (St)
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a listed stock
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Initial share price (S0)
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the share price at the product trade date (and time)
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Strike (K)
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95%
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Final Redemption at Maturity
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At maturity, the investor will receive:
- in cash, if ST/S0; > = K;
- shares where KxS0/N, otherwise.
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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):
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Scenario
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Final share price ST
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Condition test
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Final redemption for the investor
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1
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96
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96/100 > 95%
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Investor will receive cash of $1,000
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2
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90
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90/100 < 95%
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Investor will receive shares instead of cash; the number of shares is $1000/(95% x $100) = 10.52
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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%.