Model Risk Embedded in Yield Curve Construction Methods
Areski Cousin (Université Lyon 1, France)
Joint work with Ibrahima Niang and Véronique Maume-Deschamps

Thursday June 5, 11:30-12:00 | session 7.6 | Risk Management | room L

In this paper, we analyze the set of term-structure curves (interest-rate or credit term-structures) which are perfectly compatible with market quotes (interest-rate products or CDS spreads) and which do not generate any arbitrage opportunity. We first provide AOA bounds for spot interest rates and risk-neutral default probabilities at the most liquid maturities. We then show how mean-reverting affine term-structure models can be used to assess model risk embedded in yield curve construction methods. This framework is based on a piecewise-constant specification of the long-term mean parameter which allows to perfectly reproduce market price of standard vanilla IR and CDS products. Two particular families of affine term-structure models are investigated: OU driven by Lévy processes and CIR processes. We give conditions on the implied parameters for the model to be free of arbitrage opportunity. Finally, we propose a mathematical tool based on Sobol indices to study the contribution of each parameter on the term-structure uncertainty. As for IR curves, illustrations are provided in a single-curve and in a multi-curve environment. We also show how this methodology can be used to study model risk in the assessment of counterparty risk, where risk-neutral default distribution has been stripped from CDS spreads at several standard maturities.

Measuring herd behavior in stock markets
Daniël Linders (KU Leuven, Belgium)
Joint work with Jan Dhaene and Wim Schoutens

Thursday June 5, 12:00-12:30 | session 7.6 | Risk Management | room L

Never put all your eggs in one basket. Investors are well aware of this advice and prefer to compose a blend of different stocks to invest in. This is a prudent strategy because heavy losses in one asset can be countered by gains of others. However, this diversification effect is fading away when there is an increased co-movement between the stocks. It is well documented that periods of increased co-movement are tied to periods of high market stress. As a result, the diversification benefit is evaporating when it is needed the most. Therefore, having a notion about the strength of the co-movement between stock prices gives market participants the opportunity to take the necessary cautionary actions. In this paper, we construct two general frameworks to determine the implied degree of co-movement between stock prices.
Index options are traded and their prices can be observed in the market. The index option curve gives information about the real market situation. However, it is also possible to construct a second, synthetic, index option curve. This curve represents the index option curve which would be observed if the components of the stock market index were to move perfectly together. It can be proven that this synthetic index option curve is always an upper bound for the observed index option curve. The degree of herd behavior is measured by quantifying the gap between the two curves. Indeed, if this gap is small, the market is pricing index options as if they will be moving almost perfectly together.
We explore two possible methodologies to quantify the gap between the two option curves. A first approach is to capture each index option curve in a single number using swap rates. The corresponding Herd Behavior Index is then defined as the ratio between these two numbers. A second approach is similar to the first approach, but now distorted expectations are used instead of swap rates.

A Software Optimization Framework on Intel Architecture using Trinomial Trees
George Raskulinec (Intel Corp, USA)
Joint work with Robert Geva

Thursday June 5, 12:30-13:00 | session 7.6 | Risk Management | room L

Goal: Risk management plays a key role in FSI. Investment positions must constantly be evaluated to determine current market exposure. Trinomial trees used in conjunction with Greeks are a popular stock or bond option valuation method. The option is valued by using backward-induction on the tree, exercise assumed whenever the value, on the tree node, of the option is less than the exercise price. In addition, each Greek variable provides a sensitivity indication of the portfolio value as a function of a small change in a given underlying parameter. This paper provides a stepwise framework to optimize trinomial tree and Greek calculations on Intel® Xeon® and Intel® Xeon® Phi™ based platforms. The framework is general and is applicable to other quantitative financial applications on Intel hardware. The case study is presented to demystify the parallel programming redesign process. The case study of trinomial tree is especially valuable since the backwards walk on the tree from the leaves to the root provides a computation patterns that uses data dependencies which is semantically correct to vectorized yet incorrect to parallelize. Compare performance results on IA to GPUs.
Method: A logical framework combined with useful tools and libraries are required in order for developers to efficiently optimize existing code on IA. The first step is to profile existing code in order to identify hotspots and establish a baseline. Next, critical loops must be vectorized to utilize Intel’s vector hardware and optimized software libraries. Additional optimizations such as storing recurring calculations and cache alignment will then be applied. The final step is multithreading to benefit from core level parallelism. To a certain extent the framework is iterative and steps may require multiple passes.
Result 1: Review the baseline performance results and hotspots. Focus on critical loops and functions where a majority of time is spent.
Result 2: Discuss the concept of vectorization and vectorizeable loop patterns. Discuss the code modifications that may be required to vectorize critical loops. Review the vector vs. non-vector performance gains on Intel’s latest hardware and compiler.
Result 3: Ensure that critical data is cache aligned. Discuss the benefits of cache blocking. Add multiple threads to critical loops. Review the multi threaded vs. single threaded performance gains on Intel multi/many core platforms.