How HSBC got better at pricing share buy-backs

Corporate share buy-backs are booming in Europe, with volumes more than doubling in recent years. Yet with growth comes complexity. Corporates are increasingly adding bespoke clauses – early execution options, time-varying maturities and floating notionals, to name a few – to their repurchase programmes. Banks now need models that can price more complex buy-back programmes quickly and accurately. 

The standard technique for pricing share buy-backs relies on partial differential equations (PDEs) to evaluate the payoff associated with the number of shares that must be delivered to the client each day. The academic literature also features some stochastic control approaches, though these are rarely used in practice. But the custom clauses clients add to the programme can push the dimensionality of the problem to a level that stochastic control and PDE approaches can’t handle. 

This is especially true in Europe, where most deals are mandate-based compared with the US market, which sees more derivatives-style transactions that give banks more flexibility around the accumulation and delivery of shares to clients. The European Union’s Market Abuse Regulation also imposes constraints on risk management and position reporting that must be modelled and reflected in the pricing. 

We think that the American Monte-Carlo approach is one of the simplest ways to incorporate very complex clauses in a minimal amount of time

Bastien Baldacci

The costs can add up, with buy-back programmes that stretch over a long period of time and have several custom clauses costing 150 to 200 basis points more than standard agreements. To have an edge in the European market, a bank needs to have a fast and reliable pricer. 

Quants at HSBC seem to have found a solution – outlined in a recent Risk.net paper – that does just that. 

“The objective of the paper is twofold,” explains Bastien Baldacci, a co-author of the paper who advises HSBC on modelling corporate derivatives. “First, it is to bridge what I think is a huge gap in the literature, where most approaches to share buy-backs are based on stochastic control, which I don’t think is suitable. Second, to show how things are done in practice and propose our American Monte-Carlo approach.”

That approach equates valuing a repurchase strategy to pricing a complex American option. This is simpler than solving PDEs and has some additional benefits. First and foremost, it produces outputs that are intuitive and easy to calculate: the number of shares that must be bought back each day is equivalent to the delta of the programme. 

The specification of the model is also versatile and can incorporate any constraints dictated by the client or regulators, provided enough simulations are run to make the output robust.  This includes replicating early exercise options, which allows the bank – after a pre-determined date – to deliver the remainder of the shares to the client and terminate the contract. 

“To do so, we perform a two-step Monte Carlo: the first step to generate an exercise boundary using a regression, and the second to value the product given the exercise boundary generated in the first run,” says Lee Russell, an equity derivative quantitative analyst at HSBC in London and co-author of the research.

The HSBC quants claim their approach is virtually immune to the curse of dimensionality and can be used to quickly price even the most complex transactions. Banks are typically given one or two days to come up with a price for repurchase deals. In that time, they must adapt their pricing model to account for bespoke clauses and get the changes approved by model validation before running the calculations. Cutting down on the time it takes to adapt and validate the pricing model can be the difference between winning or losing the deal. 

“We think that the American Monte-Carlo approach is one of the simplest ways to incorporate very complex clauses in a minimal amount of time,” says Baldacci. “It’s a way to reduce the pricing and hedging of buy-backs to that of a simple derivative product. You enter all the constraints you have, which are taken into account in the pricing, you get the valuation of the product, which gives you the discount you can offer to the client, and then apply the first derivative of this product with respect to the spot and you get the number of shares you have to buy back on a given day.” 

The authors of the paper – including Jerome Lemue, head of European corporate equity derivatives at HSBC – acknowledge that other banks may already be using Monte Carlo approaches to price share buy-backs without publicly disclosing this. Russell and Lemue have been working on their approach for four years. The most recent paper outlines an advanced version of the approach that encompasses a broader range of repurchase strategies. But it’s not the end of the story. “We fully expect to go through another iteration of enhancements in the coming year,” says Russell.

A potential avenue to improve the approach could be increasing the frequency of execution. “One thing that is not taken into account [in the current version] is the intraday execution of the buy-back,” says Baldacci, hinting that this may be the subject of the team’s future research.