Corridor options and arc-sine law

We study a generalization of the arc-sine law. In particular we provide new results about the distribution of the time spent by a BM with drift inside a band, giving the Laplace transform of the characteristic function. If one of the extremes of the band goes to infinity, our formula agrees with the results given in Akahori and Takacs. We apply these results to the pricing of exotic option contracts known as corridor derivatives. We then discuss the inversion problem comparing different numerical methods

A market-consistent framework for the fair evaluation of insurance contracts under Solvency II

The entry into force of the Solvency II regulatory regime is pushing insurance companies in engaging into market consistence evaluation of their balance sheet, mainly with reference to financial options and guarantees embedded in life with-profit funds. The robustness of these valuations is crucial for insurance companies in order to produce sound estimates and good risk management strategies, in particular, for liability-driven products such as with-profit saving and pension funds. This paper introduces a Monte Carlo simulation approach for evaluation of insurance assets and liabilities, which is more suitable for risk management of liability-driven products than common approaches generally adopted by insurance companies, in particular, with respect to the assessment of valuation risk

Pricing discretely monitored Asian options under Levy processes

We present methodologies to price discretely monitored Asian options when the underlying evolves according to a generic Lévy process. For geometric Asian options we provide closed-form solutions in terms of the Fourier transform and we study in particular these formulas in the Lévy-stable case. For arithmetic Asian options we solve the valuation problem by recursive integration and derive a recursive theoretical formula for the moments to check the accuracy of the results. We compare the implementation of our method to Monte Carlo simulation implemented with control variates and using different parametric Lévy processes. We also discuss model risk issues

Default risk premium in credit and equity markets

The default risk premium expresses the difference between the actual default risk of a company and the default risk implied by the securities issued by the company. In this paper, we study the simultaneous relationship between the dynamics of the default risk premium and both the dynamics of the stock price and the CDS (Credit Default Swap) spread of a company. We show that an increase in the default risk premium can be associated, at the same time, to either an increase in the stock price and a decrease in the CDS spread, or to a decrease in the stock price and an increase in the CDS spread. We document that the first type of relationship features securities belonging to a consistent risk-return framework, while the second type of relationship describes securities following a counterintuitive risk-return puzzle. We show this result theoretically end empirically, by adopting a contingent claim model. We estimate the model with a non-linear Kalman filter in conjunction with quasimaximum likelihood, and we shed light on the relationship over time between the default risk premium and both the equity value and the CDS spreads for a sample of non-financial firms

Counterparty credit risk in a multivariate structural model with jumps

We present a multivariate version of a structural default model with jumps and use it in order to quantify the bilateral credit value adjustment and the bilateral debt value adjustment for equity contracts, such as forwards, in a Merton-type default setting. In particular, we explore the impact of changing correlation between names on these adjustments and study the effect of wrong-way and right-way risk

A Gentle Introduction to Value at Risk

This paper is an introduction to the measurement of market risk in financial markets, with examples drawn mainly from commodity markets. In particular, we present the concept of VaR, its limits, the problems related to its estimation and backtesting. This is done at single asset and at portfolio level. Issues related to estimation error, measurement of portfolio risk contribution and how to cope with derivative positions are also considered. Other important issues like liquidity, operational and credit risk will not be dealt here. For a Gentle introduction to the measurement of counterparty credit risk see the companion paper by Ballotta, Fusai and Marena always available on the SSRN web site

Sovereign Credit Risk in a Hidden Markov Regime - Switching Framework. Part 2

This research applies a discrete-time Markov-modulated model to default probability estimation and adapts it to Merton\u2019s contingent claims approach, backing the hypothesis that a regime-switching framework which allows for structural shifts can substantially improve the underestimation of default probabilities associated with the Merton structural model. The modeling apparatus is applied to sovereign risk proving that the methodology can be tractably extended to a contingent claims approach, and is investigated as a followup paper to an extensive methodology found in the previous edition of the Capco Journal of Financial Transformation (37) [Potgieter and Fusai (2013)]. CDS quotes are used to calibrate the regime switching model and are then used to estimate sovereign assets in both developed and emerging markets

Approximate Pricing of Swaptions in Affine and Quadratic Models

This paper proposes new bounds on the prices of European-style swaptions for affine and quadratic interest rate models. These bounds are computable whenever the joint characteristic function of the state variables is known. In particular, our lower bound involves the computation of a one-dimensional Fourier transform independently of the swap length. In addition, we control the error of our method by providing a new upper bound on swaption price that is applicable to all considered models. We test our bounds on different affine models and on a quadratic Gaussian model. We also apply our procedure to the multiple curve framework. The bounds are found to be accurate and computationally efficient

Analytical pricing of discretely monitored Asian-style options: Theory and application to commodity markets

We compute an analytical expression for the moment generating function of the joint random vector consisting of a spot price and its discretely monitored average for a large class of square-root price dynamics. This result, combined with the Fourier transform pricing method proposed by Carr and Madan [Carr, P., Madan D., 1999. Option valuation using the fast Fourier transform. Journal of Computational Finance 2(4), Summer, 61–73] allows us to derive a closed-form formula for the fair value of discretely monitored Asian-style options. Our analysis encompasses the case of commodity price dynamics displaying mean reversion and jointly fitting a quoted futures curve and the seasonal structure of spot price volatility. Four tests are conducted to assess the relative performance of the pricing procedure stemming from our formulae. Empirical results based on natural gas data from NYMEX and corn data from CBOT show a remarkable improvement over the main alternative techniques developed for pricing Asian-style options within the market standard framework of geometric Brownian motion

A Gentle Introduction to Default Risk and Counterparty Credit Modelling

In this paper we introduce the reader to the basic tools for the computation of Counterparty Credit Risk such as Credit Value Adjustment and Debt Value Adjustment. We also present the effect of mitigating clauses, like netting and collateral, in reducing the credit exposure. Detailed numerical examples are presented with reference to commodity derivatives