US2016335720A1PendingUtilityA1
Device, method and system of pricing financial instruments
Est. expiryJan 4, 2030(~3.4 yrs left)· nominal 20-yr term from priority
Inventors:David Gershon
G06Q 40/06G06Q 40/04
59
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Claims
Abstract
Some demonstrative embodiments include methods, devices and systems of pricing financial instruments. In one embodiment, a pricing module may be configured to receive first input data corresponding to at least one parameter defining a first option on an underlying asset and second input data corresponding to at least one current market condition relating to said underlying asset, and, based on said first and second input data, to determine a price of the first option according to a volatility smile satisfying a first criterion relating to a sum of a first correction corresponding to the first option and a second correction corresponding to a second option representing a position opposite to a position of a the first option and having substantially a same absolute delta value as the first option, wherein the first correction relates to a difference between a theoretical price of the first option and the price of the first option according to the volatility smile, and wherein the second correction relates to a difference between a theoretical price of the second option and the price of the second option according to the volatility smile. Other embodiments are described and claimed.
Claims
exact text as granted — not AI-modified1 . (canceled)
2 . A system comprising:
at least one interface to interface over a communication network with at least a trading system and a market data system; and a processor configured to determine at least one price of a first option on an underlying asset, based on a model price of the first option according to a pricing model, the at least one price of the first option comprising at least one price selected from the group consisting of a bid price of the first option, and an offer price of said first option, the processor configured to trigger transmission of a trade of the first option to be submitted to the trading system via the communication network, the trade comprising the at least one price of the first option, the processor configured to process real time market data from the market data system to detect a change in one or more parameters corresponding to the underlying asset, the processor configured to, based at least on the detected change in the one or more parameters, automatically recalculate at least one updated price of the first option, and automatically trigger transmission of an updated trade of the first option to be submitted to the trading system via the communication network, the updated trade comprising the at least one updated price of the first option, wherein the model price of the first option satisfies a first criterion and a second criterion, the first criterion relating to a sum of a first correction corresponding to the first option and a second correction corresponding to a second option, and the second criterion relating to a difference between the first correction corresponding to the first option and the second correction corresponding to the second option, wherein the second option represents a position opposite to a position of the first option and has a same absolute delta value as the first option, wherein the first correction relates to a difference between the model price of the first option and a price of the first option according to a Black-Scholes model with an At-The-Money (ATM) volatility, and wherein the second correction relates to a difference between a model price of the second option according to the pricing model and a price of the second option according to the Black-Scholes model with the ATM volatility.
3 . The system of claim 2 , wherein said processor is to automatically recalculate the at least one updated price of the first option based at least on a change in the model price of said first option.
4 . The system of claim 2 , wherein said processor is to automatically recalculate the at least one updated price of the first option based at least on a change in a price of said underlying asset.
5 . The system of claim 2 , wherein the processor is to determine the model price of said first option based on first data corresponding to at least one parameter defining the first option, and second data corresponding to at least one current market condition relating to said underlying asset.
6 . The system of claim 5 , wherein said first data comprises an indication of at least one parameter selected from the group consisting of a type of said first option, an expiration date of said first option, a trigger for said first option, and a strike of said first option.
7 . The system of claim 5 , wherein said second data comprises an indication of at least one parameter selected from the group consisting of a spot value, a forward rate, an interest rate, a volatility, an at-the-money volatility, a delta risk reversal, a delta butterfly, a delta strangle, a 10 delta risk reversal, a 10 delta butterfly, a 10 delta strangle, a 25 delta risk reversal, a 25 delta butterfly, a 25 delta strangle, a caplet, a floorlet, a swap rate, a security lending rate, and an exchange price.
8 . The system of claim 2 , wherein the first criterion requires that the sum of the first and second corrections is proportional to a sum of first and second volatility convexities corresponding to the first and second options,
and wherein the second criterion requires that a difference between the first and second corrections is proportional to a difference between first and second delta convexities corresponding to the first and second options.
9 . The system of claim 8 , wherein the first criterion requires that the sum of the first and second corrections is proportional to the sum of the first and second volatility convexities according to a first proportionality function, which is based on said delta,
and wherein the second criterion requires that the difference between the first and second corrections is proportional to the difference between the first and second delta convexities according to a second proportionality function, which is based on said delta.
10 . The system of claim 2 , wherein the first and second criteria require satisfying the following equations:
ζ
C
Δ
+
ζ
P
Δ
=
A
(
Δ
)
·
Vega
Δ
d
1
2
(
1
σ
K
Call
+
1
σ
K
Put
)
ζ
C
Δ
-
ζ
P
Δ
=
B
(
Δ
)
·
Vega
Δ
d
1
S
t
(
1
σ
K
Call
+
1
σ
K
Put
)
wherein ζ C Δ and ζ P Δ denote said first and second corrections,
wherein Δ denotes said delta,
wherein A(Δ) and B(Δ) denote first and second functions of A,
respectively,
wherein Vega Δ denotes a vega of the first and second options,
wherein t denotes a time to expiration of said first option,
wherein d 1 denotes a predefined function of the time to expiration of said first option,
wherein S denotes a price of said underlying asset,
and wherein σ K Call and σ K Put denote a volatility of the first option and a volatility of the second option, respectively.
11 . The system of claim 2 , wherein said first option includes a Vanilla option.
12 . The system of claim 2 , wherein said underlying asset comprises a financial asset.
13 . The system of claim 2 , wherein said underlying asset is related to at least one asset type selected from the group consisting of a commodity, a stock, a bond, a currency, an interest rate, and the weather.
14 . A product including a non-transitory storage medium having stored thereon instructions that, when executed by a machine, result in:
determining at least one price of a first option on an underlying asset, based on a model price of the first option according to a pricing model, the at least one price of the first option comprising at least one price selected from the group consisting of a bid price of the first option, and an offer price of said first option; triggering submission of a trade of the first option to a trading system via a communication network, the trade comprising the at least one price of the first option; processing real time market data from a market data system to detect a change in one or more parameters corresponding to the underlying asset; and based at least on the detected change in the one or more parameters, automatically recalculating at least one updated price of the first option, and automatically triggering submission of an updated trade of the first option to the trading system via the communication network, the updated trade comprising the at least one updated price of the first option, wherein the model price of the first option satisfies a first criterion and a second criterion, the first criterion relating to a sum of a first correction corresponding to the first option and a second correction corresponding to a second option, and the second criterion relating to a difference between the first correction corresponding to the first option and the second correction corresponding to the second option, wherein the second option represents a position opposite to a position of the first option and has a same absolute delta value as the first option, wherein the first correction relates to a difference between the model price of the first option and a price of the first option according to a Black-Scholes model with an At-The-Money (ATM) volatility, and wherein the second correction relates to a difference between a model price of the second option according to the pricing model and a price of the second option according to the Black-Scholes model with the ATM volatility.
15 . The product of claim 14 , wherein the instructions result in automatically recalculating the at least one updated price of the first option based at least on a change in the model price of said first option.
16 . The product of claim 14 , wherein the instructions result in determining the model price of said first option based on first data corresponding to at least one parameter defining the first option, and second data corresponding to at least one current market condition relating to said underlying asset.
17 . The product of claim 14 , wherein the first criterion requires that the sum of the first and second corrections is proportional to a sum of first and second volatility convexities corresponding to the first and second options,
and wherein the second criterion requires that a difference between the first and second corrections is proportional to a difference between first and second delta convexities corresponding to the first and second options.
18 . The product of claim 14 , wherein the first and second criteria require satisfying the following equations:
ζ
C
Δ
+
ζ
P
Δ
=
A
(
Δ
)
·
Vega
Δ
d
1
2
(
1
σ
K
Call
+
1
σ
K
Put
)
ζ
C
Δ
-
ζ
P
Δ
=
B
(
Δ
)
·
Vega
Δ
d
1
S
t
(
1
σ
K
Call
+
1
σ
K
Put
)
wherein ζ C Δ and ζ P Δ denote said first and second corrections,
wherein Δ denotes said delta,
wherein A(Δ) and B(Δ) denote first and second functions of Δ, respectively,
wherein Vega Δ denotes a vega of the first and second options,
wherein t denotes a time to expiration of said first option,
wherein d 1 denotes a predefined function of the time to expiration of said first option,
wherein S denotes a price of said underlying asset,
and wherein σ K Call and σ K Put denote a volatility of the first option and a volatility of the second option, respectively.Join the waitlist — get patent alerts
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