# SOLUTIONS ONLY - ComputingChallenge C++/Java - Any Takers?

#### ExSan

MERTON EQUATIONS
attached document
All values are known, except V and sigma v. -sv-
Find the values of V and sigma v? What kind of methods you will suggest?
E = V N(d1) - exp(-rT)*F*N(d2)
d1 =[ ln(V/F) + (r+0.5(sv)(sv))T ] / [ sv * sqrt(T)]
d2 = d1 - sv sqrt(T)
sE = (V/E) N(d1) sv
N(.) is the cumulative standard normal distribution

#### Attachments

• MertonEquations.pdf
11.8 KB · Views: 65

#### alain

##### Older and Wiser
do you have a set of inputs that we can compare to? I have done this in Excel already.

#### ExSan

Hi Alain
These are some of my ouputs:
I
C++:
                                               Fri Nov 14 14:15:46 2008
EXSAN v3.18.kk - [EMAIL="exsan.software@gmail.com"]exsan.software@gmail.com[/EMAIL]   [EMAIL="exsan@uio.satnet.net"]exsan@uio.satnet.net[/EMAIL]

E X S A N     M E N U
F Forum Solver
d Merton Equations
sigma_e  ---> 0.698799
r  ---> 0.578974
E  European call option  ---> 99
F  strike  K---> 100
T  ---> 15

[B](V) asset price S =       99.017     (sigma_v) asset volatility sigma  = 0.69868[/B]

Verify using The Black-Scholes European call option formula
Input data values:   s -> 99.017   k --> 100   stdev --> 0.69868
r --> 0.57897  tao --> 15
d1 = 4.5587    d2 = 1.8528
Black-Scholes, European call option value ----> 99
N(d1) =            1   sigma_e' =  0.70574     confidence / error sigma_e' = 0.99314%

EXIT FROM EXSAN                            Fri Nov 14 14:18:44 2008

II
C++:
                                               Fri Nov 14 14:22:41 2008
E X S A N     M E N U
F Forum Solver
d Merton Equations
sigma_e  ---> 0.5555
r  ---> 0.1
E  European call option  ---> 18
F  strike  K---> 90
T  ---> 1

[B]   (V) asset price S =        99.34     (sigma_v) asset volatility sigma  = 0.10312[/B]

Verify using The Black-Scholes European call option formula
Input data values:   s -> 99.34   k --> 90   stdev --> 0.10312  r --> 0.1  tao --> 1
d1 = 1.9788    d2 = 1.8757
Black-Scholes, European call option value ----> 18
N(d1) =      0.97608   sigma_e' =  0.50327     confidence / error sigma_e' = -9.402%

EXIT FROM EXSAN                            Fri Nov 14 14:24:06 2008

III

C++:
                                               Fri Nov 14 14:25:39 2008
EXSAN v3.18.kk - [EMAIL="exsan.software@gmail.com"]exsan.software@gmail.com[/EMAIL]   [EMAIL="exsan@uio.satnet.net"]exsan@uio.satnet.net[/EMAIL]
E X S A N     M E N U
f Forum Solver
d Merton Equations
Solving Merton Equations, attached pdf
"...All values are known, except V and sigma_v ...
sigma_e  ---> 0.3
r  ---> 0.1    E  European call option  ---> 100    F  strike  K---> 100    T  ---> 1

[B]    (V) asset price S =       190.48     (sigma_v) asset volatility sigma  = 0.15749[/B]

Verify using The Black-Scholes European call option formula
Input data values:   s -> 190.48   k --> 100   stdev --> 0.15749  r --> 0.1  tao --> 1
d1 = 4.8053    d2 = 4.6478
Black-Scholes, European call option value ----> 100
N(d1) =            1   sigma_e' =  0.15749     confidence / error sigma_e' = -47.502%

EXIT FROM EXSAN                            Fri Nov 14 14:27:00 2008

#### ExSan

r150
C++:
Fri Nov 14 16:23:11 2008
EXSAN v3.18.L - [EMAIL="exsan.software@gmail.com"]exsan.software@gmail.com[/EMAIL]
E X S A N M E N U
f Forum Solver
d Merton Equations
sigma_e ---> 0.09 r ---> 0.11 E European call option ---> 100
F strike K---> 97 T ---> 3
[B]This Input Data does not lead to a Solution of the Merton Equations[/B]
'''''''''''''''''''''''''''''''''''''''''''''''
sigma_e ---> 0.11 r ---> 0.11 E European call option ---> 100
F strike K---> 97 T ---> 3
[B]This Input Data does not lead to a Solution of the Merton Equations[/B]
................................................
sigma_e ---> 0.15 r ---> 0.11 E European call option ---> 100
F strike K---> 97 T ---> 3
[B](V) asset price S = 169.74 (sigma_v) asset volatility sigma = 0.088373[/B]
Verify using The Black-Scholes European call option formula
Input data values: s -> 169.74 k --> 97 stdev --> 0.088373 r --> 0.11 tao --> 3
d1 = 5.888 d2 = 5.7349
Black-Scholes, European call option value ----> 100
N(d1) = 1 sigma_e' = 0.085722 confidence / error sigma_e' = -42.852%
0 Exit Solver
0 Exit From E X S A N
0 Exit From Pixsan/Exsan M E N U
EXSAN v3.18.L - [EMAIL="exsan.software@gmail.com"]exsan.software@gmail.com[/EMAIL]
Once in a while recycle unwanted files from c:\exsan\

EXIT FROM EXSAN Fri Nov 14 16:26:34 2008

C++:
Tue Nov 18 17:13:05 2008
EXSAN v3.18.L - [EMAIL="exsan.software@gmail.com"]exsan.software@gmail.com[/EMAIL]
E X S A N M E N U
9 Forum Solver
d Merton Equations
sigma_e ---> 0.15 r ---> 0.25
E European call option ---> 100 F strike K---> 101 T ---> 4
[B](V) asset price S = 137.16 (sigma_v) asset volatility sigma = 0.10936[/B]
Verify using The Black-Scholes European call option formula
Input data values: s -> 137.16 k --> 101 stdev --> 0.10936 r --> 0.25 tao --> 4
d1 = 6.0802 d2 = 5.8615
Black-Scholes, European call option value ----> 100
N(d1) = 1 sigma_e' = 0.11046 confidence / error sigma_e' = -26.361%
d Merton Equations
Solving Merton Equations, attached pdf
"...All values are known, except V and sigma_v ...
sigma_e ---> 0.15 r ---> 0.15
E European call option ---> 100 F strike K---> 101 T ---> 4
[B](V) asset price S = 155.43 (sigma_v) asset volatility sigma = 0.096506[/B]
Verify using The Black-Scholes European call option formula
Input data values: s -> 155.43 k --> 101 stdev --> 0.096506 r --> 0.15 tao --> 4
d1 = 5.4385 d2 = 5.2455
Black-Scholes, European call option value ----> 100
N(d1) = 1 sigma_e' = 0.097472 confidence / error sigma_e' = -35.019%
d Merton Equations
Solving Merton Equations, attached pdf
"...All values are known, except V and sigma_v ...
sigma_e ---> 0.15 r ---> 0.1
E European call option ---> 100 F strike K---> 101 T ---> 4
[B](V) asset price S = 167.7 (sigma_v) asset volatility sigma = 0.089444[/B]
Verify using The Black-Scholes European call option formula
Input data values: s -> 167.7 k --> 101 stdev --> 0.089444 r --> 0.1 tao --> 4
d1 = 5.16 d2 = 4.9811
Black-Scholes, European call option value ----> 100
N(d1) = 1 sigma_e' = 0.090339 confidence / error sigma_e' = -39.774%
0 Exit Solver
0 Exit Solver
E X S A N M E N U
0 Exit From E X S A N

Main M E N U
0 Exit From Pixsan/Exsan M E N U
EXSAN v3.18.L - [EMAIL="exsan.software@gmail.com"]exsan.software@gmail.com[/EMAIL]
Once in a while recycle unwanted files from c:\exsan\

EXIT FROM EXSAN Tue Nov 18 17:16:20 2008

#### ExSan

----sorry--- my mistake

Replies
4
Views
961
Replies
0
Views
3K
Replies
7
Views
3K
Replies
2
Views
2K
Replies
0
Views
1K