The value of a derivatives structure can only be determined by how it will be hedged
Once a company has devised its hedging strategy it can then move on to the execution stage. The hedging department will ideally have their own suite of derivative pricing tools and access to commodity market data curves, allowing them to determine the theoretical value or price of the proposed hedge.
However, upon request for a quote from a market-maker the hedger should be forewarned that any such quote will contain explicit and implicit costs, not all of them obvious at first glance. Forward market curves rarely represent prices that are available to hedgers. They are normally a ‘Mid-market’ assessment where each point is typically equidistant between the bid price and the offer price of the commodity for that point in time. Moving from the theoretical mid-market to the ‘Dealing Price’ that incorporates all of the risks assumed by the market-maker involves a number of steps that we will now explore.
The logical starting point for the calculation process is the theoretical price of the hedge structure based on current mid-market values. From there the Market-Maker will appraise each of the risks assumed by becoming a counterparty to the hedge, evaluate those risks and then embed their costs into a final quote. Competitive forces will not allow a market-maker to simply stack up all of these costs and pass them through to the end client. A skilled market-maker will consider the portfolio cross-effects of these risks and how they in aggregate would impact her existing portfolio and will skew the price so as to make it more attractive either to a buyer or to a seller. Also, in practice a sophisticated market making function will assess most of this simultaneously using electronic tools that will provide analyses of the outcome of any pricing-decision so although we are exploring each aspect sequentially here the assessments are more likely to run concurrently and run through an iterative process.
Generally, the biggest risk, and certainly the most pressing to deal with after the hedge transaction is agreed, is the market risk of the transaction. A typical hedge may consist of multiple ‘legs’ (individual derivatives), maturity dates, and even different underlying commodity types. In an ideal world, the hedge provider would be able to go into the relevant exchange or interbank market and buy or sell the identical instruments to perfectly cover the risk he has taken on. In reality this is not feasible, as certain dates and strikes may not be listed nor have adequate liquidity. Therefore, in practice, a market maker will price the market risk of the deal by distilling the whole structure into its core risk components and estimating a cost to neutralise each of these.
This distillation process decomposes the risk into distinct parts representing the underlying parameters affecting the value of a hedge structure: Delta (affected by market price), Gamma (affected by market price), Vega (affected by implied volatility), Theta (affected by time to maturity), and Rho (affected by implied discount rates).
Once the distilled position has been established, the market-maker will consider a package of trades that will in her view broadly neutralise these risk factors and estimate the cost relative to the relevant current ‘mid-market’ curve to execute.
For example, consider a hedge structure that will result in a positive vega to the market maker of $300,000 per 1 volatility point in the 1-year expiry time bucket. Let us assume that the current implied volatility for such options is bid at 24.5% and offered at 25.5% around the mid value of 25.0%, with a tradeable size (or ‘depth’) of $50,000 vega. She knows she can sell $50k vega at 24.5% and may even be able to sell some at 25% or more if she is lucky. But she needs to sell 6 rounds of $50k vega to fully immunise her vega risk, and from experience she estimates that she can likely achieve this at a weighted-average implied volatility of 24.25%. This represents a slippage of 0.75 volatility points from the current mid-market value of 25.0%. Therefore, she concludes that this will incur 0.75 x $300k = $225k of slippage (cost) to neutralise her vega risk, relative to the price derived from the mid-market implied volatility value of 25.0%. This $225k cost must then be factored into the final quoted price for the hedge. If the market-maker has some pre-existing open positions in her portfolio that are a natural offset to some of the new market risks then the slippage incurred could be reduced due to a diminished requirement to offset. There will be a slippage value for each of the major risk factors that are needed to neutralise the overall risk, and each one will be factored into the final quoted price. For risk factors such as delta which tend to be most volatile and need to be neutralised quickly, the market liquidity available at the time of day that the hedge is being transacted could become a primary concern in the calculation. Occasionally, this delta risk may be transformable into spread risk (i.e. the change in value of a derivative generated by a change in the shape of the forward curve) by stacking a greater proportion of the hedge in the earlier maturities to be rolled to longer maturities over time. She would do this to both take advantage of the greater liquidity in the front end and the lower volatility of spreads relative to the Flat Price. The ability of the market maker to take advantage of this will feature in the final dealing price.
A direct cost to a trader will be commissions that are payable per transaction to arranging agents. For Exchange traded instruments a commission per lot of instrument executed is payable and deducted from the trader’s exchange account. Similarly, for OTC transactions, the broker matching the counterpartys will make a charge based on the Notional Volume of the transaction. These can be directly built-into any pricing decision.
Alongside risks that can be directly hedged there exist ‘unhedgeable’ risks which cannot be ignored. For example, perhaps the market maker is quoting a 5 year forward hedge for a commodity that only has liquidity out for 3 years. Or, there may be some basis risk arising from the quality or location specification of the hedge. Again, she will judge at what price she is willing to take on and warehouse this risk and adjust the final hedge price accordingly.
Where the hedge is being transacted Over-The-Counter, that is to say bilaterally between the hedger and the market-maker, each entity is taking on the credit risk of the other performing on the hedge transaction. Even if the hedger has a superior credit rating to the market-maker, the market-maker is still taking on credit risk to the hedger and will need to account for the cost of hedging this credit exposure. As discussed in our last article, use of a Credit Support Annexe can reduce this credit exposure by entering a Variation Margin agreement. The cost of hedging the credit risk arising from the hedge is normally determined by the price of insuring the maximum expected (negative) exposure of the hedge using Credit Default Swaps linked to the hedger. In many cases some or all of the cost of this element of the hedge will also play a vital part in the final dealing price.
The cost of funding during the life of the transaction and, in the case of financial institutions, regulatory capital, also play a vital role in the dealing price assessment. The market-maker’s activity relies on her ability to access funding to post margin, and, for a bank, the risk that she takes on as counterparty to the hedge will require regulatory capital to be allocated against it. Both come at a cost to the market-maker. Funding Value Adjustment (FVA) arises due to the difference in interest rates paid to the market-maker’s treasury department for the initial and variation margin and the rate paid to the market-maker on the margin by the counterparty or clearing house. Capital Value Adjustment (commonly referred to as KVA and sometimes referred to as RWA, Risk Weighted Assets) relates to the cost associated with holding the required regulatory capital against the hedge transaction. The implementation of the Basel Accords has led to stricter requirements for banks to allocate risk-absorbing capital against the risk taken. Like all entities, a bank has a cost of capital, and the cost of the portion of capital allocated for regulatory purposes against the hedge transaction must be incorporated into the dealing price.
There are some risks that are hard to quantify but which should also be a consideration. Political risk would fit this description. As an extreme example consider how, after most UN sanctions on Iran were lifted in early 2016, the French energy company Total positioned itself to develop natural gas assets in the country. Subsequently the election of President Trump in the U.S.A. led to that country performing a volte-face on its Iran stance, tearing up the political deal and imposing U.S. sanctions on the country. Total had little choice (if it wanted to continue to do business in the U.S., and to use the USD international payment system) but to walk away from those investments at considerable cost. A market-maker would need to think very carefully about entering into a hedge with a company in such a jurisdiction even if it is completely legal at the time, and at the very least would need to price that political risk into his quote. Within Banks the riskiness of a country would attract a greater allocation of Regulatory Capital thereby raising its cost. For non-bank organisations operating sophisticated risk frameworks, the internal return hurdles will be appropriately adjusted for this risk by an internal credit-rating process.
Finally, it’s important to consider the trader’s own ‘Axe’ (his or her market view) and how this will impact a final dealing price. The integration of this factor will skew the price either in favour of a potential buyer or in favour of a potential seller of the structure according to the trader’s will.
There are indirect costs such Exchange membership fees, costs of licences and permits, building rents, and costs of operations but these cannot be attributable to any individual transaction and are not therefore part of an individual dealing price. Instead this cost will be estimated in aggregate over a longer time period (typically a year) and absorbed into a return on capital hurdle. The higher the overheads the higher this return hurdle is likely to be.
Once all the items above have been added to the theoretical mid-market price, we have arrived at a ‘risk-neutral’ quote. That is, a value that incorporates the price of the primary risks that the market maker is assuming. In theory though, this quote is a ‘break-even’ price whereas the market-maker is running a business with a target return on equity. She will hence add what she deems a fair profit margin onto the quote, based on internal return requirements. The definition of ‘fair’ is up for negotiation between the hedger and the market-maker, but this article has hopefully given the hedger a starting point for that discourse.
A visualisation of a hypothetical situation where a market maker is assessing the offer price of a hedge structure on Crude Oil.
In this illustration, the DVA, KVA, the Stack & Roll, Portfolio Effects, and the Axe are negative since if this trade were absorbed into the trader’s portfolio each of these would reduce costs.