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We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on $q$-binomial (or Kemp) random walks, with application to default with logistic failure rates. This model allows us to consider time-dependent switching probabilities varying according to a trend parameter on a non-self-similar binomial tree. In particular, it includes tilt and stretch parameters that control increment sizes. Option pricing formul…
In this paper, we deal with an axiomatic approach to default risk. We introduce the notion of a default risk measure, which generalizes the classical probability of default (PD), and allows to incorporate model risk in various forms. We discuss different properties and representations of default risk measures via monetary risk measures, families of related tail risk measures, and Choquet capacities. In a second step,…
We develop a tractable framework for valuing Asian options when trading the underlying generates market impact and execution costs. Starting from a discrete-time, quote-level model, we construct a reference midpoint suitable for Asian payoffs and separate market impact into a transient component and a permanent drift distortion driven by signed trading. This specification admits continuous-time limits where the midpo…
Binomial trees are widely used in the financial sector for valuing securities with early exercise characteristics, such as American stock options. However, while effective in many scenarios, pricing options with CRR binomial trees are limited. Major limitations are volatility estimation, constant volatility assumption, subjectivity in parameter choices, and impracticality of instantaneous delta hedging. This paper pr…
We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox-Ross-Rubinstein (CRR) pricing model. The main tool used in the paper for cleaning up the reasoning is applying static hedging arguments. This can be accomplished by taking various routes through some auxiliary considerations, namely Arrow-Debreu securities, digital options or backward random processe…
The model of this paper gives a convenient strategy that a bank in the federal funds market can use in order to maximize its profit in a contemporaneous reserve requirement (CRR) regime. The reserve requirements are determined by the demand deposit process, modelled as a Brownian motion with drift. We propose a new model in which the cumulative funds purchases and sales are discounted at possible different rates. We …
Credibility theory provides tools to obtain better estimates by combining individual data with sample information. We apply the Credibility theory to a Uniform distribution that is used in testing the reliability of forecasting an interest rate for long term horizons. Such empirical exercise is asked by Regulators (CRR, 2013) in validating an Internal Model Method for Counterparty Credit Risk. The main results is tha…