US2010262564A1PendingUtilityA1
Conditional Probability Method For Stock Option Valuation
Individually held — no corporate assignee on recordPriority: Jun 26, 2006Filed: Jun 22, 2010Published: Oct 14, 2010
Est. expiryJun 26, 2026(expired)· nominal 20-yr term from priority
Inventors:Richard R. Joss
G06Q 40/04G06Q 30/04G06Q 40/00G06Q 40/06
37
PatentIndex Score
0
Cited by
0
References
0
Claims
Abstract
A method, system, and computer program product for determining stock option pricing in which the interplay of short-term interest rates and expected long-term rates of return on the underlying security results are factored to yield a more accurate forecast of options prices as compared to conventional models. The method of the present invention employs an expected long-term rate of return parameter and a conditional probability volatility parameter and an adjustment factor to address the put-call parity theorem which addresses the accuracy problems of the Black-Scholes model. The method can also be applied using a known current option prices to determine an assumed long-term rate of return.
Claims
exact text as granted — not AI-modified1 . A computer implemented method for computing a stock option price for an underlying stock given historical stock prices of the underlying stock, a current stock price, a time duration, and a strike price comprising the steps of:
determining a continuously compounded extended long-term rate of return parameter; determining a risk-free rate of return; determining a volatility parameter; calculating a conditional probability volatility parameter to maintain a relationship between the volatility parameter and the long-term rate of return parameter; determining a put-call parity adjustment parameter; and computing a stock option price.
2 . The method of claim 1 , wherein said step of computing a stock option price further comprises maintaining a relationship between the volatility parameter and the long-term rate of return parameter.
3 . A computer implemented method of valuating at a current time an estimated call option price given a current stock price S, historical prices of the stock, a strike price K, a time duration t, an estimated volatility σ, an estimated continuously compounded expected long-term rate of return of the stock g, and a current continuously compounded risk-free rate of return r, the method comprising the steps of:
calculating
a
conditional
probability
volatility
parameter
v
=
2
g
σ
2
2
g
+
σ
2
;
calculating
d
1
=
ln
(
S
/
K
)
+
(
g
+
v
2
2
)
t
v
t
;
calculating
d
2
=
d
1
-
v
t
;
determining
put
-
call
parameter
A
=
-
g
t
;
determining
put
-
call
parameter
B
=
g
t
;
solving OP c =SN(d 1 )−Ke −gt N(d 2 )−K(e −rt −e −gt (w) for OP c to obtain the predicted call option price, where w=1.00 if Ke −gt /S≦A and w=0.00 if Ke −gt /S≧B, and OP c is determined by linear interpolation for values of Ke −gt /S between A and B.
4 . The method of claim 3 , wherein said step of linear interpolation of OP c is calculated as
OP
c
(
K
)
=
(
K
-
AS
gt
)
(
OP
c
(
BS
gt
)
)
+
(
BS
gt
-
K
)
(
OP
c
(
AS
gt
)
)
BS
gt
-
AS
gt
.
5 . The method of claim 4 , further comprising the step of calculated a predicted put option price OP p for values of K between ASe gt and BSe gt , as OP p (K)=OP c (K)−S+Ke −rt .
6 . A computer implemented method of valuating at a current time an estimated put option price given a current stock price S, historical prices of the stock, a strike price K, a time period t, an estimated volatility σ, an estimated continuously compounded expected long-term rate of return of the stock g, and a current continuously compounded risk-free rate of return r, the method comprising the steps of:
calculating
a
conditional
probability
volatility
parameter
v
=
2
g
σ
2
2
g
+
σ
2
;
calculating
d
1
=
ln
(
S
/
K
)
+
(
g
+
v
2
2
)
t
v
t
;
calculating
d
2
=
d
1
-
v
t
;
determining
put
-
call
parameter
A
=
-
g
t
;
determining
put
-
call
parameter
B
=
g
t
;
solving OP p =SN(d 1 )−Ke − gt N(d 2 )−(S−Ke gt )+K(e −rt −e −gt )(1−w) for OP p to obtain the predicted put option price for values of K<ASe gt or K>BSe gt .
7 . A computer implemented method of determining an expected long-term rate of return g given the current call option price OP c , current put option price OP p , the current stock price S, a strike price K, a time period t, an estimated volatility σ, and a current continuously compounded risk-free rate of return r, the method comprising the steps of:
solving OP c =SN(d 1 )−Ke −gt N(d 2 )−K(e −rt −e −gt )(w) where w=1.00 if Ke −gt /S≦A and w=0.00 if Ke −gt /S≧B, OP c is determined by linear interpolation for values of Ke −gt /S between A and B, for g.
8 . A computer readable medium containing program instructions for execution on a computer system, which when executed by a computer causes the computer to perform method steps for valuating at a current time an estimated call option price given a current stock price S, historical prices of the stock, a strike price K, a time duration t, an estimated volatility σ, an estimated continuously compounded expected long-term rate of return of the stock g, and a current continuously compounded risk-free rate of return r, the method comprising the steps of:
calculating
a
conditional
probability
volatility
parameter
v
=
2
g
σ
2
2
g
+
σ
2
;
calculating
d
1
=
ln
(
S
/
K
)
+
(
g
+
v
2
2
)
t
v
t
;
calculating
d
2
=
d
1
-
v
t
;
determining
put
-
call
parameter
A
=
-
g
t
;
determining
put
-
call
parameter
B
=
g
t
;
solving OP c =SN(d 1 )−Ke −gt N(d 2 )−K(e −rt −e −gt )(w) for OP c to obtain the predicted call option price, where w=1.00 if Ke −gt /S−A, w=0.00 if Ke −gt /S≧B, and OP c is determined by linear interpolation for values of Ke −gt /S between A and B.
9 . The medium of claim 8 , wherein in said method performed by said instructions said step of linear interpolation of OP c is calculated as
OP
c
(
K
)
=
(
K
-
AS
gt
)
(
OP
c
(
BS
gt
)
)
+
(
BS
gt
-
K
)
(
OP
c
(
AS
gt
)
)
BS
gt
-
AS
gt
.
10 . The medium of claim 9 , wherein said method further comprises the step of calculated a predicted put option price OP p for values of K between ASe gt and BSe gt , as OP p (K)=OP c (K)−S+Ke −rt .
11 . A computer readable medium containing program instructions for execution on a computer system, which when executed by a computer causes the computer to perform method steps for valuating at a current time an estimated put option price given a current stock price S, historical prices of the stock, a strike price K, a time period t, an estimated volatility σ, an estimated continuously compounded expected long-term rate of return of the stock g, and a current continuously compounded risk-free rate of return r, the method comprising the steps of:
calculating
a
conditional
probability
volatility
parameter
v
=
2
g
σ
2
2
g
+
σ
2
;
calculating
d
1
=
ln
(
S
/
K
)
+
(
g
+
v
2
2
)
t
v
t
;
calculating
d
2
=
d
1
-
v
t
;
determining
put
-
call
parameter
A
=
-
g
t
;
determining
put
-
call
parameter
B
=
g
t
;
solving OP p =SN (d 1 )−Ke −gt N(d 2 )−(S−Ke −gt )+K(e −rt −e −gt )(1−w) for OP p to obtain the predicted put option price for values of K<ASe gt or K>BSe gt .
12 . A computer readable medium containing program instructions for execution on a computer system, which when executed by a computer causes the computer to perform method steps for determining an expected long-term rate of return g given the current call option price OP c , current put option price OP p , the current stock price S, a strike price K, a time period t, an estimated volatility σ, and a current continuously compounded risk-free rate of return r, the method comprising the steps of:
solving OP c =SN(d 1 )−Ke −gt N(d 2 )−K(e −rt −e −gt )(w) where w=1.00 if Ke −gt /S≦A and w=0.00 if Ke −gt /S≧B, OP c is determined by linear interpolation for values of Ke −gt /S between A and B, for g.Join the waitlist — get patent alerts
Track US2010262564A1 — get alerts on status changes and closely related new filings.
We store only your email — no account needed. See our privacy policy.