Method and system for modeling volatility
A method for determining the implied volatility of a swap option employs intuitive factors to arrive at a close approximate of volatility. The volatility curve is a convex shaped curve which more closely follows real market volatility than previous methods. The slope of the curve is provided by employing a premium model which allows for a correlation between rates and volatility. The convex shaped curve is arrived by assuming a lognormal distribution for the underlying volatility.
1. A computer implemented method for financial decisioning using a computer system generating a premium for an option and making a decision based on the generated premium, the option providing a right to transact with respect to an underlying asset, the method comprising:
inputting information into the computer system, the information including:
an average volatility of the asset by employing historical or market data;
a volatility of volatility of the asset by employing historical data; and
a type of distribution for the forward rate based on historical data;
providing a volatility distribution graph based on the selected distribution type, the volatility and the volatility of volatility, the volatility distribution graph having volatility as the x-axis and probability as the y-axis;
dividing the volatility distribution graph into a plurality of vertical slices, each of said slices corresponding to a volatility, whereby the integration of the volatility distribution graph over the volatility range corresponding to each slice provides a probability for the corresponding volatility;
determining an option premium for each vertical slice by employing a volatility premium calculation equation implemented by a computer processor of the computing system;
weighing each premium from said determining of premium step by the probability associated with the corresponding volatility as determined from the volatility distribution graph; and
summing all weighed premiums associated with the volatilities to provide a premium for the option, wherein the volatility premium calculation equation used to determine the stochastic volatility premium incorporates a trader-selected q to calculate the value of a call option on rate r with forward value r , strike k, expiration time t, and annualized volatility σ and is given by the following formula:
BSQ
(
r
_
,
c
,
σ
,
t
)
=
r
_
1
q
·
Φ
(
d
1
)
+
r
_
(
1
-
1
q
-
k
~
)
·
Φ
(
d
2
)
Where Φ is the normal cumulative inverse function and
k
~
=
k
/
r
_
x
~
=
-
1
q
ln
[
(
k
~
-
1
)
q
+
1
]
/
(
σ
t
)
d
1
=
x
~
+
1
2
q
σ
t
d
2
=
x
~
-
1
2
q
σ
t
.
2. The method of claim 1 , further comprising performing, using the computer processor, an inverse Black procedure to determine the conventional market implied volatility for a strike rate that is different from the forward rate.
3. The method of claim 2 , further comprising computing, using the computer processor, the market price based on the convention market implied volatility and comparing the generated premium to the market price.
4. The method of claim 3 , further comprising generating a decision, using the computer processor, to buy or sell the option based on the comparison.