Valuation
 

Valuation

Valuation of linear deals

Fundamentally all commodities deals are swaps, whereby one receives one leg and pays the other one. Tying it back to the generic trade template, the mark to market of a trade results from the steps detailed below. Upfront payments such as premiums or fees come on top of MTM to obtain the overall profit & loss.


Swap valuation
l
Swap valuation
Level Component Description Notation
Trade
Trade net present value Discounted PnL. The difference of the NPV of both legs. NPV=(NPV l0−NPV l1)×LS \rm NPV = ( NPV_{\space l_0} - NPV_{\space l_1} ) \times LS
Trade value Non discounted trade value. V=((V l0×Q l0)−(V l1×Q l1))×LS \rm V = ( ( V_{\space l_0} \times Q_{\space l_0}) - ( V_{\space l_1} \times Q_{\space l_1} ) ) \times LS
Trade intrinsic value The difference between the market rate of both legs.
Moneyness, unitary 'margin', non-probability weighted 'premium'.
The sign depends on trade direction: long minus short leg.		 IV=(F l0−F l1)×LS \rm IV = ( F_{\space l_0} - F_{\space l_1} ) \times LS
Legl
Leg net present value The sum of the discounted estimated future cash flows of all periods of the leg. NPV l= ∑p=1P (NPV l,p×Q l,p)∑p=1PQ l,p \rm NPV_{\space l} = \frac {\space \sum_{ p=1 }^P \space ( NPV_{\space l,p} \times Q_{\space l,p})} { \sum_{ p=1 }^P Q_{\space l,p} }
Leg rate
  • For single-period trades leg rate means period rate.
  • For multi-period rates, it equals the quantity weighted average of the period rates.
 R l= ∑p=1P (R l,p×Q l,p)∑p=1PQ l,p \rm R_{\space l} = \frac {\space \sum_{ p=1 }^P \space ( R_{\space l,p} \times Q_{\space l,p})} { \sum_{ p=1 }^P Q_{\space l,p} }
Leg market rate F l= ∑p=1P (F l,p×Q l,p)∑p=1PQ l,p \rm F_{\space l} = \frac {\space \sum_{ p=1 }^P \space ( F_{\space l,p} \times Q_{\space l,p})} { \sum_{ p=1 }^P Q_{\space l,p} }
Periodp
Period net present value Value corrected by discount factor between flow settlement date and evaluation date. NPV l,p=V l,p×D l,p \rm NPV_{\space l,p} = V_{\space l,p} \times D_{\space l,p}
Period value Rate times quantity. V l,p=R l,p×Q l,p \rm V_{\space l,p} = R_{\space l,p} \times Q_{\space l,p}
Period rate Net rate, multiplied by rate factor then incremented by rate margin.
Values of those are most often respectively 1 and 0, hence equal to net rate.		 R l,p=(F l,p×RF l,p)+RM l,p \rm R_{\space l,p} = (F_{\space l,p} \times RF_{\space l,p}) + RM_{\space l,p}
Period market rate, Price
  • For a floating leg, the market rate for the observed period.
  • For a fix leg, the trade price (strike).
 F l,p \rm F_{\space l,p}