Assignment 3 - revise & comments to Colman's codes

[Eric Tang]

Colman,

Based on our discussion in class last Saturday, I completed the coding
of Q1 on Sunday. However, when moving on to Q2, I found that the
calculation of Basket Call Option was wrong. [for RiskMetric model,
please refer to the file "RiskMetric Wikipedia.pdf"

The initial value of the basket of call options of Q2 is 12.336. This
value should be comparable to the initial value of the Basket Call
option. Therefore, our original value of 43.35 is too high.

Because we are asking to calculate the value of the Basket Call option
at maturity. Therefore, by definition, the initial value of the option
is equal to the present value of the expected value at maturity (this
is exactly the same backward method we used in the binomial tree
model).

I modified the program and find out the initial value of the Basket
Call is ~13.5 (a value similar to the basket of call case). The
simulated mean and VaR is ~riskfreerate and -100% (79% VaR, total
loss). I think the results is correct by the fact that;
1. The expected return of a well diversified portfolio is
riskfreerate.
2. If this is true. Then the expected V(T) = K * exp(riskfreerate *
T). Therefore, it is most likely V(T) > K, i.e. C = Max(V(T)-K, 0) =
0.
3. Because there are certain number of C = 0 events during the MC
cycles, the corresponding returns are (0 - C(0))/C(0) = -1. In this
case, the resultant standard deviation of return > 1.

The revised Assign 3 Excel ("cen_assign_3_1.xls") file includes Q2
too. Similar to "risk_v2_2.xls" there are four types of VaR
calculation:
1. MC
2. Historical
3. VC
4. MC_DV
Please go through the codes to see if they are correct. Thx.

PS: If you have time you may help to make the layout and buttons more
presentable.

Eric

Eric

[Eric Tang]

Correction:

2. If this is true. Then the expected V(T) = K * exp(riskfreerate *

T). Therefore, it is most likely V(T) > K, i.e. C = Max(V(T)-K, 0).
However, if the standard deviation is large. Then C=0 for V(T) < K.
3. ... The fact that there are events of return = -1. Number of MC
(nsim) must be large enough for data convergence.

[Colman Yeung]

Hi Eric,   For question 1, I don't think we need to calculate the present value for the option basket for calculating the mean and VaR. What's your opinion?   Regards Colman --- On Mon, 7/19/10, Eric Tang <ecm...@gmail.com> wrote:

[Eric Tang]

Colman,

Because the return is calculated from the initial option value. Therefore, if it is too large. Then it will make the calculated mean and standard deviation very small. I know a small mean and VaR is comparable to the Q2 basket of calls. However, remember the Q2 is for 1-day 95%VaR. But Q1 is for VaR at maturity. They are different. Moreover, I find no literature or document to support that Basket call option can be calculated by using Black Scholes formula. On the other, there is a paper mentioned that sum of lognormal distributions is not lognormal. In this case, BS does not apply to the pricing of this option. 

I have also finished tidying up the layout and VBA of the Excel file ("cen_assign_3_2 uploaded to the Group"). Data has been run and will complete the result analysis before or in the class. 

Eric