Forward Volatility Agreements 
Use
A forward volatility agreement is a forward transaction that is based on the volatility of an exchange rate. The forward volatility agreement is an agreement to buy or sell a straddle on a future date. A straddle is a combination of a call option and a put option that have the same underlying, exercise date and strike price. The term of the option starts on the forward date.
The strike of the straddle is fixed to the date on which the term of the options begins, and at the same time the forward spot is set for the exercise date of the straddle. The premium of the forward volatility agreement is also calculated and paid on the forward date. The forward volatility fixed at the start of the contract is taken as the basis.
Integration
You create forward volatility agreements as generic transactions. For more information see Creating Forward Volatility Agreements .
Features
The amount paid for the forward volatility agreement is calculated as follows:
where N is the nominal value of the forward volatility agreement, σ is the current volatility, σ fix is the agreed volatility, V straddle is the value of the options.
The calculation rule is applied only if the horizon date is before or on the forward date. If the horizon date is after the forward date, the value of the forward volatility agreements is zero. The following formula provides the value v FVA for a purchase of a straddle for the forward date: The sign (+/-) changes for a sale.
( )
where
s(t)
is the spot price of the underlying of the straddle,
r(t
1
,t
2
)
is the risk-free interest rate for the period
t
1
through to
t
2
,
q(t
1
,t
2
)
is the dividend rate for the period
t
1
through to
t
2
,
σ
fix
is the volatility agreed on the contract date,
σ(t,t
F
,T)
is the forward volatility at time point
t
for the period
t
F
through to
T
, and
N(x)
is the cumulative normal distribution. Continuous compounding is used for interest rate
r
and dividend rate
q
; yield curve
r(t
E
,T)
is used for forward rate
r(t,T)
, in which
t
E
is the evaluation date. The current forward volatility is calculated as follows:
If the underlying of the straddle is an exchange rate, r is the risk-free interest rate for the local currency, and q the risk-free interest rate for the foreign currency. The spot value s(t) is the product of the amount in local currency, which is paid when the straddle matures, and the exchange rate valid on evaluation date t E .
The calculation rule uses the Black-Scholes formula for pricing options. This formula first prices the components of the straddle - the call and put options - by using the forward interest rates and the current forward volatility. The values for the straddles are totaled and discounted, and the option premiums are deducted. This results in the calculation rule shown above for forward volatility agreements, in which the premium of the term is given by the fixed volatility σ fix .
The calculation rule for forward volatility agreements applies where you use the same market data for the bid and ask rates. If this is not the case, the system uses a calculation rule that has separate premium calculation for the bid and ask rates.