Option pricing
Being particular about calibration
Following previous work on the calibration of multi-factor local stochastic volatility models to market smiles, Julien Guyon and Pierre Henry-Labordère show how to calibrate exactly any such model. Their approach, based on McKean’s particle method,…
Q&A: Myron Scholes on LTCM, crisis lessons and the value of intermediation
Quants received a lot of flak for the crisis, but the profession is on the cusp of a golden age, according to Myron Scholes, co-inventor of the Black-Scholes pricing model. In an interview with Laurie Carver, he also criticises post-crisis regulation,…
Pricing, Basel, Paulson & Co: the top stories of 2011 so far
A review of the top Risk.net stories during the first half of 2011
Repricing the cross smile: an analytic joint density
Derivatives contracts on multiple foreign exchange rates must be priced to avoid arbitrage by contracts on the cross-rates. Given the triangle of smiles for two underlyings and their cross, Peter Austing provides an analytic formula for a joint…
Marking systemic portfolio risk with the Merton model
The downside risk of a portfolio of assets is generally substantially higher than the downside risk of its components. In times of crisis, when assets tend to have high correlation, the understanding of this difference can be crucial in managing the…
Multi-currency CSA chaos behind push to standardised CSA
A major split has emerged between dealers over how to price derivatives backed by multi-currency CSAs. Some banks are looking to arbitrage disparities in valuations as a result, causing back-loading of trades to central counterparties to slow to a…
Stressed in Monte Carlo
Stress tests are playing a bigger role in the operation of financial institutions, both from a risk management and a regulatory perspective. But Monte Carlo can behave badly when fed extreme parameters and give misleading results. Here, Christian Fries…
Volatility interpolation
Developing an arbitrage-free, consistent volatility surface in both expiry and strike from a discrete set of option quotes is a difficult and computationally intense problem. In this article, Jesper Andreasen and Brian Huge use a non-standard variant of…
Multi-currency CSA chaos behind push to standardised CSA
A major split has emerged between dealers over how to price derivatives backed by multi-currency CSAs. Some banks are looking to arbitrage disparities in valuations as a result, causing back-loading of trades to central counterparties to slow to a…
Isda working group to draw up new, standardised CSA
Derivatives market set for shake-up as confusion over how to price multi-currency CSA trades drives a push towards a standardised collateral agreement
Choice of collateral currency
Collateral agreements are becoming popular in the over-the-counter derivatives market. Masaaki Fujii and Akihiko Takahashi demonstrate its significant impact on derivatives pricing with a direct link to the cross-currency market. The importance of…
Choice of collateral currency
Collateral agreements are becoming popular in the over-the-counter derivatives market. Masaaki Fujii and Akihiko Takahashi demonstrate its significant impact on derivatives pricing with a direct link to the cross-currency market. The importance of…
Trade of the month: Digital payoffs
Digital options lead to two outcomes and are most commonly used with capital protected structured products.
Correlations in asynchronous markets
Lorenzo Bergomi addresses the issue of pricing multi-asset options in the context of asynchronous markets. Using the criterion that the carry profit and loss (P&L) vanishes, he derives the expression of the correlation estimator for the asynchronous case…
US inflation options sponsored forum: Recovery and development
The inflation market has had a challenging few months. In particular, many dealers were hurt by short positions in 0% inflation floors, causing sizeable losses for some firms. Sponsored by BGC Partners, Risk convened a panel of major inflation dealers in…
Sponsored statement: The problems with generally used interpolation spaces
In a world increasingly focused on effective enterprise-level risk management, there are notable discrepancies in volatility management techniques. Murex proposes a cross-asset interpolation space with potentially significant risk management impacts
The inflation pricing conundrum
Fear of a spike in consumer prices has created greater demand for inflation protection from a variety of participants. This has increased the need for inflation pricing and analytics tools – but it is not as simple as tweaking existing models used for…
Expanded smiles
Implementing models with stochastic as well as deterministic local volatility can be challenging. Here, Jesper Andreasen and Brian Huge describe an expansion approach for such models that avoids the high-dimensional partial differential equations usually…
Interview with Vladimir Piterbarg
Vladimir Piterbarg talks about his new article published in the Cutting Edge section of Risk magazine
Funding beyond discounting: collateral agreements and derivatives pricing
Standard theory assumes traders can lend and borrow at a risk-free rate, ignoring the intricacies of the repo and collateralisation markets. Here, Vladimir Piterbarg shows that these force adjustments to discounting, forward prices and implied…
Smile dynamics IV
Lorenzo Bergomi addresses the relationship between the smile that stochastic volatility models produce and the dynamics they generate for implied volatilities. He introduces a new quantity, the skew stickiness ratio (SSR), and shows how, at order one in…
Last option before the armageddon
Damiano Brigo and Massimo Morini show how the pricing of credit index options depends on the probability of a financial portfolio 'armageddon'. They introduce a new equivalent pricing measure that lays the foundation for a market model framework in multi…