Fair Value Adjustment(FVA)- Bid Offer Reserve

Bid offer reserve is the exit cost of the portfolio. It is the cost in terms of bid offer spread to be paid when we want to close the positions. The banks value the trades at mid price [(bid +offer)/2]. But when the desk has to close the long(buy) position , the trade is closed at less than mid price and vice versa. Usually bid offer reserves are risk based.

Here is the formula:
Bid Offer Reserve = – Absolute( risk * half bid offer spread).

Different risk types:
a. FX Delta = FX exposure – Not only generated from FX Forwards/NDF and FX Options but Non USD swaps, swaptions, CDS , Deposit/Loans in Non USD.
b. IR Delta = Interest rate PV01 – Interest risks mainly swaps and swaptions. FX products can have significant IR delta which is Zero (base) curve and Basis curve (cross currency) . Interest rate curves are in each currency and Basis risks. There are Bond basis risk curves as well. Usually bond bid offer is calculated is price based and bond basis risk is excluded.
c. CR Delta = Credit CS01 – Risk on Credit Default Swap curve . There can be significant bid offer spread on CDS curve especially EM Sovereign and corporates.
d. Vega = ATM and Smile Vega – Vega is from all kinds of options products, FX Options, Cap, Floor, Swaptions, Options and Option on Credit default swaps and many more options products including Hybrid products.

Bid offer reserve on Exchanged traded products and Bonds can be price based unless hedged against OTC trades. As per Bank’s policy the bid offer reserve is calculated. If OTC and Exchange markets are segregated, then the bid offer reserve is calculated separately which would be higher charge to the P&L.

The above formula looks simple but in real life there are many issues and complexities.
Here are the few reasons:
1. Market data input vs Risks output: The market data sourced from vendors are in raw forms. They are cleaned, formatted, structured and calibrated. This refined market data used to value the derivatives. Hence, the risk output from the system may or may not be in the raw form. For example interest rate curve consist of many swaps, futures underlying overlapping, but IR delta is not as granular and more tenors formatted. FX volatility ATM, RR , and ST are calibrated to generate volatility surface. So the Vega can be in different form than the raw market data sourced originally. The Valuation Control Group(VCG) must review the market data feed and final risks output. Ensure the all trades risks are captured (completeness), netting vs non-netting, ATM Vega and smile Vega. Once, the appropriate risks are determined and captured, the next step is to use appropriate bid offer spread. The bid offer spread will be in original market data sourced in raw format. Hence, the matching of correct bid offer spread to the right risk by each tenor or any other parameters is essential.
2. Cash products vs Derivatives products. There can be segmented markets for cash vs derivatives products for the same asset class. Commodity physical spot/deposit trade vs Forwards/Swaps on commodities. They can not be netted out and calculate the bid offer reserve separately for cash products which is mostly based on notional and derivatives products mainly interest rate (PV01) delta.
3. Different Asset Classes: The desk can be mainly for Foreign exchange which just not trades FX forwards/NDF, FX Options, exotic options. There are hedges which can be vanilla swaps, cross currency swaps, futures , options on futures. It need to ensure that the FX delta, IR delta , IR Basis deltas and Vegas are properly netted. If the desk is using Interest rate futures to hedge IR delta from main FX business. Then the IR delta from FX and IR futures must be netted appropriately.
4. Tenors Netting: IR delta (PV01) are netting across buckets short , mid and long term risks. Then the bid offer reserve is calculated using appropriate bid offer spread. For example 2M to 1Y risk can be offsetting and can be netted which reduces the total risk for short term and eventually reduces the bid offer reserve. The tenor netting does happen on Vega risk across the volatility surface.
5. Currency pair netting: In foreign exchange business, the currency pairs are grouped as the per their strong base currency and time zone. This again reduces the overall risk and finally the bid offer reserve.
6. ATM and Smile Vega Netting: Volatility surface is used to value options, swaption and all other volatility driven products. There are ATM Vega as well smile Vega (e.g. Risk Reversal and ST Vega). The bid offer reserve calculated on ATM as well smile Vega. As per the model , valuation control group calculate the reserve. The model can use correlation between tenors , currency pair etc. FX, IR delta (base , basis curves) and Credit delta (CS01) risks are still simple after taking care of above netting and other factors. Risk generated from Volatility surface is in matrix form. There has to be appropriate model which ensures that the appropriate netting and bid offer spread must be used even the formula remain simple in nutshell.