How replication simplifies pricing of vol exotics

Barclays quants replicate knock-out corridor swaps using barrier options in bid to make pricing easier

Dealers in Asia have a problem. Retail structured products such as autocallables add vega risk to their books. But the hedge they came up with five years ago – the corridor variance swap – is not an ideal solution.

Corridor variance swaps provide payments to the investor based on the realised variance of the underlying when it falls between two strikes, in exchange for a fixed payment. When the underlying moves outside of the barriers, the swaps no longer accrue the realised variance, but the investor would have to post margin anyway. In addition, the autocallables that are being hedged with these products knock out if the underlying moves beyond a certain barrier. This means the trade being hedged wipes out, but if the underlying falls back within the corridor of strike prices, the dealer would still have to pay the investor on the corridor swap.

One fix introduced by banks couple of years ago involved adding a knock-out barrier to the product that matches the knock-out barrier of the autocallable. That way, both the trade and the hedge will end when the barrier is reached.

Adding this additional feature, however, introduces modelling complexities. Simple corridor variance swaps are free of model risk because their pricing is model-agnostic. When a knock-out feature is added, this is no longer the case.

“It could be a simple Black-Scholes model, it could be a local volatility model, or it could be a stochastic volatility model; all of those models will return the same price for your product for standard variance swaps and corridor variance swaps,” says Olaf Torné, head of Asia-Pacific equity derivatives quantitative analytics at Barclays in Hong Kong. “That is a special feature of variance swaps and corridor variance swaps. That is no longer true when you introduce a knock-out barrier, which means effectively model risk is inherent in this product.”

In a recent technical article, Knocking out corridor variance, Torné and Amine Ahallal, head of Japan index trading, also at Barclays in Hong Kong, propose a replication that allows users to price and risk-manage knock-out corridor variance swaps in a simpler way.

The quants achieve this by replicating the payoff of the knock-out corridor swap payoff using a hypothetical strip of barrier options, which expire worthless if the underlying hits a certain barrier. In quantitative finance, replication allows one to express the payoff of a complex product as a combination of payoffs of simpler products. This makes it easier for traders and risk managers to understand the price dynamics of a product.

In the case of the knock-out corridor swaps, replication using barrier options allows the quants to use a stochastic volatility model for the products which can be solved using a two-dimensional partial differential equation (PDE).

The method does not necessarily bring an advantage in speed. PDEs could be written on the knock-out corridor swaps even without the replication. But in that case, the PDEs would be of much higher dimension, making computation very slow, the quants argue. Simulating the price using Monte Carlo could also take similar time as the quants’ model.

The real advantage lies in the ability of the model to provide a deeper insight into the dynamics of the product. Replicating the swap with simpler products allows the bank to understand the underlying exposure in terms of risks of known products – the barrier options. This can in turn eliminate some unknowns, providing the dealer with more comfort in offering the knock-out corridor swaps.

“Initially we were not very comfortable because adding this [knock-out] feature moves you away from known replication properties of the standard corridor variance,” says Ahallal. “As far as trading is concerned, introducing a replication using existing payoffs – barrier options in this case – is very powerful as it gives you more confidence in pricing and hedging which helps in offering that product in the first place.”

One Asia-based quant at a European bank agrees the model is useful for risk management: “Even if practitioners are fully aware that it’s not feasible to trade a full portfolio of barrier options given the liquidity constraint, the intuitive decomposition allows them to develop an understanding of the various risk drivers in terms of more familiar instruments.”

The popularity of autocallables in Asian markets such as Korea, Taiwan and Japan has left dealers wary of disruptions during unfavourable market moves, as seen in the crash of 2015. This in turn has increased demand for hedges such as corridor variance swaps. Given the size of the market, users recognise the need to understand the risks of complex structures such as knock-out variance swaps.

The replication proposed by the Barclays quants brings the industry a step closer to that aim.