Hasil untuk "q-fin.PR"

E. Lepeschkin, B. Surawicz

Hardik Routray, Bernhard Hientzsch

We propose a simple methodology to approximate functions with given asymptotic behavior by specifically constructed terms and an unconstrained deep neural network (DNN). The methodology we describe extends to various asymptotic behaviors and multiple dimensions and is easy to implement. In this work we demonstrate it for linear asymptotic behavior in one-dimensional examples. We apply it to function approximation and regression problems where we measure approximation of only function values (``Vanilla Machine Learning''-VML) or also approximation of function and derivative values (``Differential Machine Learning''-DML) on several examples. We see that enforcing given asymptotic behavior leads to better approximation and faster convergence.

Ricardo T. Fernholz, Robert Fernholz

This paper presents a synthesis of the theories of portfolio generating functions and option pricing. The theory of portfolio generation is extended to measure the value of portfolios generated by positive C^{2,1} functions of asset prices X_1,... , X_n directly, rather than with respect to a numeraire portfolio. If a portfolio generating function satisfies a specific partial differential equation, then the value of the portfolio generated by that function will replicate the value of the function. This differential equation is a general form of the Black-Scholes equation. Similar results apply to contingent claim functions, which are portfolio generating functions that are homogeneous of degree 1. With the addition of a riskless asset, an inhomogeneous portfolio generating function V : R^{+n} x [0, T] \to R^+ can be extended to an equivalent contingent claim function \hat{V} : R^+ x R^{+n} x [0, T] \to R^+ that generates the same portfolio and is replicable if and only if V is replicable. Several examples are presented.

Alessandro Gnoatto, Silvia Lavagnini

We provide a general HJM framework for forward contracts written on abstract market indices with arbitrary fixing and payment adjustments, and featuring collateralization in any currency denominations. In view of this, we first provide a thorough study of cross-currency markets in the presence of collateral and incompleteness. Then we give a general treatment of collateral dislocations by describing the instantaneous cross-currency basis spreads by means of HJM models, for which we derive appropriate drift conditions. The framework obtained allows us to simultaneously cover forward-looking risky IBOR rates, such as EURIBOR, and backward-looking rates based on overnight rates, such as SOFR. Due to the discrepancies in market conventions of different currency areas created by the benchmark transition, this is pivotal for describing portfolios of interest-rate products that are denominated in multiple currencies. As an example of contract simultaneously depending on all the risk factors that we describe within our framework, we treat cross-currency swaps using our proposed abstract indices.

Libo Li, Ruyi Liu, Marek Rutkowski

We study the upper and lower bounds for prices of European and American style options with the possibility of an external termination, meaning that the contract may be terminated at some random time. Under the assumption that the underlying market model is incomplete and frictionless, we obtain duality results linking the upper price of a vulnerable European option with the price of an American option whose exercise times are constrained to times at which the external termination can happen with a non-zero probability. Similarly, the upper and lower prices for an vulnerable American option are linked to the price of an American option and a game option, respectively. In particular, the minimizer of the game option is only allowed to stop at times which the external termination may occur with a non-zero probability.

Baron Law

A simple method is proposed to estimate the instantaneous correlations between state variables in a hybrid system from the empirical correlations between observable market quantities such as spot rate, stock price and implied volatility. The new algorithm is extremely fast since only low-dimension linear systems are involved. If the resulting matrix from the linear systems is not positive semidefinite, the shrinking method, which requires only bisection-style iterations, is recommended to convert the matrix to positive semidefinite. The square of short-term at-the-money implied volatility is suggested as the proxy for the unobservable stochastic variance. When the implied volatility is not available, a simple trick is provided to fill in the missing correlations. Numerical study shows that the estimates are reasonably accurate, when using more than 1,000 data points. In addition, the algorithm is robust to misspecified interest rate model parameters and the short-sampling-period assumption. G2++ and Heston are used for illustration but the method can be extended to other affine term structure, local volatility and jump diffusion models, with or without stochastic interest rate.

Mathieu Mercadier, Jean-Pierre Lardy

Credit Default Swap (CDS) levels provide a market appreciation of companies' default risk. These derivatives are not always available, creating a need for CDS approximations. This paper offers a simple, global and transparent CDS structural approximation, which contrasts with more complex and proprietary approximations currently in use. This Equity-to-Credit formula (E2C), inspired by CreditGrades, obtains better CDS approximations, according to empirical analyses based on a large sample spanning 2016-2018. A random forest regression run with this E2C formula and selected additional financial data results in an 87.3% out-of-sample accuracy in CDS approximations. The transparency property of this algorithm confirms the predominance of the E2C estimate, and the impact of companies' debt rating and size, in predicting their CDS.

Chris Kenyon, Mourad Berrahoui

We introduce Climate Change Valuation Adjustment (CCVA) to capture climate change impacts on CVA+FVA that are currently invisible assuming typical market practice. To discuss such impacts on CVA+FVA from changes to instantaneous hazard rates we introduce a flexible and expressive parameterization to capture the path of this impact to climate change endpoints, and transient transition effects. Finally we provide quantification of examples of typical interest where there is risk of economic stress from sea level change up to 2101, and from transformations of business models. We find that even with the slowest possible uniform approach to a climate change impact in 2101 there can still be significant CVA+FVA impacts on interest rate swaps of 20 years or more maturity. Transformation effects on CVA+FVA are strongly dependent on timing and duration of business model transformation. Using a parameterized approach enables discussion with stakeholders of economic impacts on CVA+FVA, whatever the details behind the climate impact.

Nicolas Essis-Breton, Patrice Gaillardetz

This article presents fast lower and upper estimates for a large class of options: the class of constrained multiple exercise American options. Typical options in this class are swing options with volume and timing constraints, and passport options with multiple lookback rights. The lower estimate algorithm uses the artificial intelligence method of lookahead search. The upper estimate algorithm uses the dual approach to option pricing on a nearest-neighbor basis for the martingale space. Probabilistic convergence guarantees are provided. Several numerical examples illustrate the approaches including a swing option with four constraints, and a passport option with 16 constraints.

Rüdiger Frey, Kevin Kurt, Camilla Damian

Several proposals for the reform of the euro area advocate the creation of a market in synthetic securities backed by portfolios of sovereign bonds. Most debated are the so-called European Safe Bonds or ESBies proposed by Brunnermeier, Langfield, Pagano,Reis, Van Nieuwerburgh and Vayanos (2017). The potential benefits of ESBies and other bond-backed securities hinge on the assertion that these products are really safe. In this paper we provide a comprehensive quantitative study of the risks associated with ESBies and related products, using an affine credit risk model with regime switching as vehicle for our analysis. We discuss a recent proposal of Standard and Poors for the rating of ESBies, we analyse the impact of model parameters and attachment points on the size and the volatility of the credit spread of ESBies and we consider several approaches to assess the market risk of ESBies. Moreover, we compare ESBies to synthetic securities created by pooling the senior tranche of national bonds as suggested by Leandro and Zettelmeyer(2019). The paper concludes with a brief discussion of the policy implications from our analysis.

Jing Peng, Ronald J. Williams

T. Crook, E. Feher, G. Larrabee

Stefania Gabrielli, Andrea Pallavicini, Stefano Scoleri

Valuation adjustments are nowadays a common practice to include credit and liquidity effects in option pricing. Funding costs arising from collateral procedures, hedging strategies and taxes are added to option prices to take into account the production cost of financial contracts so that a profitability analysis can be reliably assessed. In particular, when dealing with linear products, we need a precise evaluation of such contributions since bid-ask spreads may be very tight. In this paper we start from a general pricing framework inclusive of valuation adjustments to derive simple evaluation formulae for the relevant case of total return equity swaps when stock lending and borrowing is adopted as hedging strategy.

Jin Sun, Kevin Fergusson, Eckhard Platen et al.

In this paper we consider the pricing of variable annuities (VAs) with guaranteed minimum withdrawal benefits. We consider two pricing approaches, the classical risk-neutral approach and the benchmark approach, and we examine the associated static and optimal behaviors of both the investor and insurer. The first model considered is the so-called minimal market model, where pricing is achieved using the benchmark approach. The benchmark approach was introduced by Platen in 2001 and has received wide acceptance in the finance community. Under this approach, valuing an asset involves determining the minimum-valued replicating portfolio, with reference to the growth optimal portfolio under the real-world probability measure, and it both subsumes classical risk-neutral pricing as a particular case and extends it to situations where risk-neutral pricing is impossible. The second model is the Black-Scholes model for the equity index, where the pricing of contracts is performed within the risk-neutral framework. Crucially, we demonstrate that when the insurer prices and reserves using the Black-Scholes model, while the insured employs a dynamic withdrawal strategy based on the minimal market model, the insurer may be underestimating the value and associated reserves of the contract.

T. Tanabe, M. Notomi, E. Kuramochi et al.

Kun Wang, Yinglei, Ark-Chew Wong et al.

C. Nguyen, R. Howe

E. Bourinet, T. Soong, K. Sutton et al.

L. Cherfils, Y. Il’yasov

A. Loy, Lendie Follett, H. Hofmann

Abstract In statistical modeling, we strive to specify models that resemble data collected in studies or observed from processes. Consequently, distributional specification and parameter estimation are central to parametric models. Graphical procedures, such as the quantile–quantile (Q–Q) plot, are arguably the most widely used method of distributional assessment, though critics find their interpretation to be overly subjective. Formal goodness of fit tests are available and are quite powerful, but only indicate whether there is a lack of fit, not why there is lack of fit. In this article, we explore the use of the lineup protocol to inject rigor into graphical distributional assessment and compare its power to that of formal distributional tests. We find that lineup tests are considerably more powerful than traditional tests of normality. A further investigation into the design of Q–Q plots shows that de-trended Q–Q plots are more powerful than the standard approach as long as the plot preserves distances in x and y to be the same. While we focus on diagnosing nonnormality, our approach is general and can be directly extended to the assessment of other distributions.