Value Vanilla FX Options Here
The Vanilla FX Option Pricer allows its user to price a "Plain Vanilla" FX Option, i.e., either a European Call or a European Put.
The Strike (aka Exercise Price) of the option may be specified either:
- directly, as a Strike Value
- as a ratio of Strike to the Forward Rate
- as a Delta Target. In that latter case, the pricer will seek the Strike that corresponds to the specified Delta Target
- as the "At-The-Money" Strike: either the "At-The-Money-Forward" or the "Zero-Delta Straddle" Strike
Input
Page
The input page layout is as follows:
The
inputs are:
Currency Pair:
a drop-down list allowing the user to select the currency pair of
the option
Payoff Type:
a drop-down list allowing the user to select either a Call or a Put
option
Maturity:
a drop-down list allowing to user to select either:
Exercise Date:
an input box for the user to input the date in the day, month, year
format, only to be used if the selected maturity is "Actual Exercise Date"
Moneyness Type:
a drop-down list allowing the user to select either:
Actual Strike, i.e., an actual value for the option's exercise price
Ratio of the Strike to the Forward Rate, i.e., the ratio of the option' strike to the Forward FX Rate
Left-Hand-Side
Delta (protects option value in the underlying currency). The pricer will automatically adjust the Strike so that the option's Left-Hand-Side Delta be equal to the specified target
Right-Hand-Side
Delta (protects option value in the numéraire currency). The pricer will automatically adjust the Strike so that the option's Right-Hand-Side Delta be equal to the specified target
Exercise Price
or Delta: an input box
for the user to enter either the desired Strike or the Delta target, depending
on the selected Moneyness Type. If no input is provided, then the pricer selects the At-The-Money Strike: either the Forward Rate (if Moneyness Type is not Delta) or the Zero-Delta Straddle Strike (if Moneyness Type is Delta)
Pricing
is achieved by clicking on the “Next”
button.
Pricing Results
The
pricing output is as follows.
Revalued at Market Close as of: Thu 13 Oct 2011
USDJPY CALL
|
Currency Pair
|
USDJPY (Japanese Yen per US Dollar)
|
|
Option Type
|
USD CALL / JPY PUT
|
|
Strike
|
JPY 76.3359 per USD of Notional Amount
|
|
Exercise Date
|
Mon 15 Oct 2012
|
|
Forward FX Rate
|
JPY 76.3359 per USD of Notional Amount
|
|
Volatility
|
12.8389 %
|
Premium and Greeks
|
Option Value (Premium)
|
USD 5.11 = JPY 393.19 per USD 100 of Notional Amount
|
|
Option Spot Delta (dValue/dSpot)
|
USD value-sensitivity (LHS): USD 47.15, JPY value-sensitivity (RHS): USD 52.26, per USD 100 of Notional Amount
|
|
Option Forward Delta (dFwdValue/dFwd)
|
USD value-sensitivity (LHS): USD 47.43, JPY value-sensitivity (RHS): USD 52.57, per USD 100 of Notional Amount
|
|
Option Gamma (d2Value/dSpot2)
|
USD value-sensitivity (LHS): 3.38, JPY value-sensitivity (RHS): 3.99, per USD 100 of Notional Amount
|
|
Option Vega (dValue/dVol)
|
USD 0.3983 = JPY 30.6499 per % vol increase per USD 100 of Notional Amount
|
|
Option Theta (dValue/dTime)
|
USD 0.0 = JPY -0.44 per calendar day per USD 100 of Notional Amount
|
|
Option Vanna (dVega/dSpot)
|
USD 0.0026 = JPY 0.1991 per USD of Notional Amount
|
|
Option Volga (dVega/dVol)
|
USD -0.0128 = JPY -0.9918 per USD of Notional Amount |
The
“Premium and Greeks”
section gives the following information:
Value
(or Premium): this is
the present value of the option, i.e., the premium that the dealer
asks her client to pay to buy the option1
Delta:
this is the sensitivity (first derivative) of the option's value
(with respect) to the Spot FX Rate:
Left-Hand-Side
Delta (LHS) denotes when the
option's value is expressed in the underlying
currency, for example the USD in a USDJPY Call2
Right-Hand-Side
Delta (RHS) denotes when the
option's value is expressed in the numéraire
currency, for example the JPY in a USDJPY Call
Gamma:
this is the sensitivity of the Delta to the Spot FX Rate
Vega:
this is the sensitivity of the option's value to the Volatility of
the FX Rate
Theta:
this is the sensitivity of the option's value to the passage of
time, otherwise known as the Time Decay
Vanna:
this is the sensitivity of the vega to the Spot FX Rate
Volga:
this is the sensitivity of the Vega to the volatility of the FX Rate
All
results are given per unit of Notional Amount.
The Notional Amount is the amount of the
underlying asset
concerned by the option, for example “a 1-year $1 million USD call
at JPY 73.5”.
This
is the option3
to buy $1M worth of JPY at a price of JPY 73.5 per US Dollar, in one
year.
The
inventory of an
options' trader is always denominated in terms of the Greeks.
These quantities express the risk to which the trader's portfolio of
options is exposed. For the Wikipedia explanation of Greeks, please Click Here
For the Wikipedia explanation of Vanilla FX Options along with a Case Study, please Click Here
__________________________________________________
1 Commercial
margin considerations left aside
2 As
the option's value is expressed in the numéraire, the
Left-Hand-Side Delta corresponds to the first derivative of the
option value divided by the Spot FX rate with respect to the Spot FX
Rate. It is different from the Right-Hand-Side Delta, i.e., the
first derivative of the the option value with respect to the Spot FX
Rate.
3 i.e.,
the right, not the obligation
(c) Reference Derivatives 2011
