Interest Rates

struct Numeraire <: Leaf
    obs_time::ModelTime
    curve_key::String
end

The price of our numeraire asset price N(t) at observation time t.

Typically, this coincides with the bank account price in numeraire (i.e. domestic) currency.

struct BankAccount <: Leaf
    obs_time::ModelTime
    key::String
end

The price of a continuous compounded bank account B(t) at observation time t and with unit notional at inception.

struct ZeroBond <: Leaf
    obs_time::ModelTime
    maturity_time::ModelTime
    key::String
end

The price of a zero coupon bond P(t,T) with observation time t and bond maturity time T.

struct Fixing <: Leaf
    obs_time::ModelTime
    key::String
end

The value of an index fixing Idx(t) at observation time t.

The value is obtained from a term structure linked to the path.

struct LiborRate <: Leaf
    obs_time::ModelTime
    start_time::ModelTime
    end_time::ModelTime
    year_fraction::ModelValue
    key::String
end

A simple compounded forward Libor rate.

LiborRate(
   obs_time::ModelTime,
   start_time::ModelTime,
   end_time::ModelTime,
   key::String,
   )

A simple compounded forward Libor rate with year fraction from model time.

struct CompoundedRate <: Payoff
    obs_time::ModelTime
    start_time::ModelTime
    end_time::ModelTime
    year_fraction::ModelValue
    fixed_compounding::Union{Payoff, Nothing}
    key::String
    fixed_type::DataType  # distinguish from constructors
end

A continuously compounded backward looking rate.

This is a proxy for daily compounded RFR coupon rates.

For obstime less starttime it is equivalent to a Libor rate.

CompoundedRate(
    obs_time::ModelTime,
    start_time::ModelTime,
    end_time::ModelTime,
    key::String,
    fixed_compounding::Union{Payoff, Nothing} = nothing,
    )

A continuously compounded backward looking rate with year fraction from model time.

struct Optionlet <: Payoff
    obs_time::ModelTime
    expiry_time::ModelTime
    gearing_factor::Payoff
    forward_rate::Union{LiborRate, CompoundedRate}
    strike_rate::Payoff
    call_put::ModelValue
end

The time-t forward price of an option paying [ϕ(R-K)]^+. Rate R is determined at expiry_time. The rate R can be forward-looking or backward-looking.

forward price is calculated as expectation in T-forward measure where T corresponds to the period end time. Conditioning (for time-t price) is on information at obs_time.

The rate R is written in terms of a compounding factor C and R = [G C - 1]/τ. Here, G is an additional gearing factor to capture past OIS fixings.

Then, option payoff becomes G/τ [ϕ(C - (1 + τK)/G)]^+.

Optionlet(
    obs_time_::ModelTime,
    expiry_time::ModelTime,
    forward_rate::Union{LiborRate, CompoundedRate},
    strike_rate::Payoff,
    call_put::ModelValue,
    gearing_factor::Payoff = ScalarValue(1.0),
    )

Create an Optionlet payoff.

struct Swaption <: Payoff
    obs_time::ModelTime
    expiry_time::ModelTime
    settlement_time::ModelTime
    forward_rates::AbstractVector
    forward_rate_pay_times::AbstractVector
    fixed_times::AbstractVector
    fixed_weights::AbstractVector
    fixed_rate::ModelValue
    payer_receiver::ModelValue
    disc_key::String
    zcb_pay_times::AbstractVector
    rate_type::DataType  # to distinguish from functions
end

Time-t forward price of an option paying An⋅[ϕ(S-K)]^+. Swap rate S is determined at expiry_time. Floating rates in S can be forward looking of backward looking rates.

Forward price is calculated in T-forward measure where T corresponds to settlement_time. Conditioning (for time-t price) is on information at obs_time.

Swaption(
    obs_time_::ModelTime,
    expiry_time::ModelTime,
    settlement_time::ModelTime,
    forward_rates::AbstractVector,
    fixed_times::AbstractVector,
    fixed_weights::AbstractVector,
    fixed_rate::ModelValue,
    payer_receiver::ModelValue,
    disc_key::String,
    )

Create a Swaption payoff.