The paper calculates fair strike for variance swaps on time-changed Markov processes.
problem Calculating fair strike for variance swaps on time-changed Markov processes.
method Proving the fair strike equals the price of a European contract and solving the integro-differential equation.
result The fair strike for variance swaps can be computed explicitly for certain Markov processes.
Combines option pricing and portfolio theory for optimal hedging.
problem Optimal hedging of European options in various price dynamics.
method Derives optimal holdings and unhedged risk for different price dynamics.
result Derives solutions for various price dynamics including binomial, diffusion, volatility, volatility-of-volatility, and jump diffusion.
A version of indifference valuation of a European call option is proposed that includes statistical regularities of nonstochastic randomness. Classical relations (forward contract value and Black-Scholes formula) are obtained as particular cases. We show that in the general case of nonstochastic randomness the minimal …
We offer new formulas for European option pricing under tempered stable processes.
problem Pricing European options under tempered stable processes.
method Series expansions for tempered stable densities and European option prices.
result Our formulas are hyperparameter-free and competitive with traditional methods.
Two new models improve option valuation for negative or mean reverting futures markets.
problem Valuation of futures contracts with negative underlying prices.
method Proposed two models: Ornstein-Uhlenbeck and continuous time GARCH.
result Improved option values compared to Black 76, especially for negative or mean reverting markets.
Study geometric step options with jumps, deriving pricing equations and characterizations.
problem Pricing geometric step options in markets with jumps.
method Symmetry and parity relations, partial integro-differential equations, ordinary integro-differential equations.
result Derive semi-analytical pricing results for geometric step options.
Study bounds for prices of European and American options with optional termination.
problem Bounding prices of options with potential termination.
method Duality results linking upper prices of vulnerable options to American options with constrained exercise times.
result Linking upper prices of vulnerable options to American options and game options.
Paper evaluates different models for predicting credit default swap volatility.
problem Predicting the Implied Volatility of credit default swaps.
method SVM, Gradient Boosting, and Attention-GRU Hybrid model.
result Identifies strengths in classical and SOTA machine learning methods.
Develops a dynamic SSVI model to prevent arbitrage and implied volatility bubbles.
problem Preventing arbitrage in implied volatility models.
method Dynamic SSVI parameterization ensuring European vanilla option prices are martingales.
result No model allows for arbitrage-free implied volatility bubbles.
The paper presents an approximate formula for European mortgage options pricing.
problem Pricing European mortgage options with accuracy and efficiency.
method Approximation of the underlying price distribution using lognormal distributions and matching moments.
result The proposed formula provides a good approximation with high accuracy compared to Monte Carlo simulations.
Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount found many applications in finance. Closed-form solutions for the price of these options have appeared in the literature for the case when the contract underlying asset follows a geometric Brownia…
Network science reveals corruption risk in EU procurement markets.
problem Identifying corruption risk in EU procurement markets.
method Analyzing a large dataset of public procurement contracts using network science.
result Corruption risk is clustered and varies by country, not just by market core or periphery.
Study on time-zero efficiency of European power derivatives markets using statistical tests and trading rules.
problem Assessing time-zero efficiency in European power derivatives markets.
method Statistical tests based on the law of one price and trading rules based on price differentials and no-arbitrage violations applied to daily data of three European power markets.
result Definite conclusions on time-zero efficiency are not possible for French and Spanish markets due to liquidity and representativeness challenges.
In this paper, we search whether the Benford's law is applicable to monitor daily changes in sovereign Credit Default Swaps (CDS) quotes, which are acknowledged to be complex systems of economic content. This test is of paramount importance since the CDS of a country proxy its health and probability to default, being a…
Optimal exercise boundary for put options with delivery lags identified.
problem Analyzing the optimal exercise time for American put options with delivery lags.
method Decomposing the option into a European put and a new American-style derivative, using free boundary techniques.
result The optimal exercise boundary exists and is a strictly increasing and smooth curve.
The paper prices and replicates various financial contracts on a risky asset with stochastic volatility and jumps.
problem Pricing and replicating financial contracts on assets with stochastic volatility and jumps.
method Develops pricing and hedging formulas for various financial contracts, independent of the volatility process dynamics.
result Pricing and hedging formulas for financial contracts are derived without dependence on the volatility process dynamics.
New method for non-arbitrage pricing in risky assets.
problem Non-arbitrage pricing in markets with non-negative risky assets.
method Constructing martingale measures and proving optional decomposition theorem.
result Deriving fair prices for European option contracts.
Study pricing options on forward contracts using infinite-dimensional affine models.
problem Pricing European-style options on forward contracts in complex stochastic volatility models.
method Model forward price curves using stochastic partial differential equations modulated by stochastic volatility processes. Analyze two classes of affine stochastic volatility models: Gaussian and pure-jump. Derive conditions for existence of exponential moments and develop semi-closed pricing formulas.
result Developed semi-closed Fourier-based pricing formulas for vanilla call and put options in infinite-dimensional affine models.
Paper offers fast, accurate pricing for long-dated contracts using real-world probability measure.
problem Inaccurate pricing of long-dated contracts in insurance and pension funds.
method Applies RMQ and JRMQ algorithms under real-world measure, using benchmark approach.
result Prices are less expensive than risk-neutral valuation, highlighting departure from traditional methods.
Extends pricing of American options in nonlinear markets.
problem Pricing American options in nonlinear markets.
method Detailed study of unilateral valuation problems, BSDE approach.
result Explicit pricing, hedging, and exercising results.
Study uses put-call parity to estimate cost of funding in equity derivatives markets.
problem Estimating the cost of funding in active equity derivative markets.
method Develops a method using European put and call prices to recover the implicit discount factor and cost of funding.
result Identifies the cost of funding in major equity markets, showing it is typically around 34 basis points above OIS.
Develops a fast and accurate option pricing method using Legendre polynomials.
problem Pricing European options with smoothness issues in payoff functions.
method Legendre series expansion and characteristic function relation for density function.
result Highly accurate approximations for European call options.
We introduce a multi-factor stochastic volatility model based on the CIR/Heston stochastic volatility process. In order to capture the Samuelson effect displayed by commodity futures contracts, we add expiry-dependent exponential damping factors to their volatility coefficients. The pricing of single underlying Europea…
We consider a financial contract that delivers a single cash flow given by the terminal value of a cumulative gains process. The problem of modelling and pricing such an asset and associated derivatives is important, for example, in the determination of optimal insurance claims reserve policies, and in the pricing of r…
There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study these opportunities in a generic stochastic volatility model and exhibit the strateg…
In this paper we present a new methodology for option pricing. The main idea consists to represent a generic probability distribution function (PDF) via a perturbative expansion around a given, simpler, PDF (typically a gaussian function) by matching moments of increasing order. Because, as shown in literature, the pri…
Bielecki and Rutkowski (2014) introduced and studied a generic nonlinear market model, which includes several risky assets, multiple funding accounts and margin accounts. In this paper, we examine the pricing and hedging of contract both from the perspective of the hedger and the counterparty with arbitrary initial end…
Bielecki and Rutkowski (2014) introduced and studied a generic nonlinear market model, which includes several risky assets, multiple funding accounts and margin accounts. In this paper, we examine the pricing and hedging of contract both from the perspective of the hedger and the counterparty with arbitrary initial end…
MiCA regulation led to a shift in stablecoin dominance.
problem Impact of MiCA regulation on stablecoin trading.
method Comparative analysis of regulated and non-regulated exchanges.
result USDC gained market share and trading volume post-MiCA regulation.
We develop a novel framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no-arbitrage arguments, we derive the nonlinear backward stochastic differential equations (BSDEs) associated with the replicating p…
The study models mortgage prepayment risk using stochastic housing market activity.
problem Modeling prepayment risk in mortgages under varying housing market conditions.
method Developed a stochastic model for prepayment option value, using swaption pricing formulas and non-standard actuarial hedging.
result Housing market covariance significantly impacts prepayment option prices.
Examines stress tests in European banking supervision.
problem Ensuring financial stability in European banks.
method Reviews existing financial stability institutions and stress testing.
result Stress tests are crucial for European banking supervision.
We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance (hedging risk) of the portfolio on the date of maturity of the call option we find a fraction of the ass…
This paper examines the value of a cancellable European option in a finite time horizon setting. The specifications of this generalized European option allow the seller to cancel the option at any point in time for a fixed penalty paid directly to the holder. Here, we provide an explicit valuation formula for the Europ…
New method for European option pricing faster and more robust.
problem Pricing European options efficiently and accurately.
method Fourier cosine series expansions for models with known characteristic functions.
result More robust and faster than the original COS method.
Paper proposes equal risk pricing for financial derivatives using convex risk measures.
problem Equal risk pricing and hedging in financial derivatives with convex risk measures.
method Established that the problem reduces to solving independently hedging problems for writer and buyer with zero initial capital. Provided dynamic programming equations for European and American options under Markovian decompositions of convex risk measures.
result Equal risk pricing leads to more similar and smaller risks for both writer and buyer compared to other pricing methods.
Pricing of European basket call option with n-assets and a bond is discussed in this paper, where all prices of n-assets and the bond are driven by Exponential Ornstein-Uhlenbeck processes. The close-form of European basket option pricing formula is derived. Utilizing with 1-order differential approximate numerical sol…
Study on Leverage Ratio in European banks during financial crises.
problem Impact of financial crises on European banks' Leverage Ratio.
method Empirical analysis using regression techniques.
result Leverage Ratio is significantly influenced by financial scenarios.
We use principle component analysis (PCA) of cross correlations in European government bonds and European stocks to investigate the systemic risk contained in the European economy. We tackle the task to visualize the evolution of risk, introducing the conditional average rolling sum (CARS). Using this tool we see that …
New EPS insurance offers partial protection against superannuation losses.
problem Lack of efficient investment insurance for superannuation holders.
method Developed a new financial derivative, equity protection swap (EPS), and derived a fair pricing formula.
result EPS can be an efficient investment insurance tool for superannuation accounts.
Study shows EU countries have worsening debts and deficits.
problem Worsening public debts and deficits in EU countries.
method Statistical analysis of public debts and deficits between EU and non-EU countries.
result EU countries have worse public debts and deficits than non-EU countries, especially after Euro introduction.
The paper calculates European option prices under a generalized skew normal distribution.
problem European option pricing under a generalized skew normal distribution.
method Proved existence of martingale measure, derived explicit option pricing formula, applied numerical methods.
result Explicit expressions for European option prices are derived.
Develops European power option pricing under correlated interest rate and asset processes.
problem Pricing European power options under correlated interest rate and asset processes.
method Martingale method and Girsannov transform.
result Derives European power option pricing formulae under two market assumptions.
Examines insurance market development and similarity post-2004 EU enlargement.
problem Comparing insurance markets of EU old and new members post-enlargement.
method Analyzes data from 2004 to present to compare insurance markets.
result Identifies similarities and differences in insurance markets post-2004 enlargement.
Maximizes American put price bounds using European put prices.
problem Finding upper bounds for American put prices.
method Model-free approach using European put prices and martingale transport.
result Derives a model with maximal American put price.
In the paper we develop mathematical tools of quantile hedging in incomplete market. Those could be used for two significant applications: o calculating the \textbf{optimal capital requirement imposed by Solvency II} (Directive 2009/138/EC of the European Parliament and of the Council) when the market and non-market ri…
American options can be equivalent to European options under certain conditions.
problem Determining when American options can be simplified to European options.
method Using methods from Jourdain and Martini, Chrsitensen, and convex duality.
result A first step towards verifying representability of American options.
Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or multidimensional parabolic problems of the convection-diffusion type and generaliz…