Pricing of Securities
This paper will demonstrate some new techniques for developing the theory of Asian (arithmetic average) options pricing. We discuss the basic derivation of the diffusion equations, and how various techniques from potential theory can be…
Researchers have been using Neural Networks and other related machine-learning techniques to price options since the early 1990s. After three decades of improvements in machine learning techniques, computational processing power, cloud…
Equity-linked securities with a guaranteed return become very popular in financial markets ether as investment instruments or life insurance policies. The contract pays off a guaranteed amount plus a payment linked to the performance of a…
We develop an open-source tool (EmTract) that extracts emotions from social media text tailed for financial context. To do so, we annotate ten thousand short messages from a financial social media platform (StockTwits) and combine it with…
Panoptic is the perpetual, oracle-free, instant-settlement options trading protocol on the Ethereum blockchain. Panoptic enables the permissionless trading of options on top of any asset pool in the Uniswap v3 ecosystem and seeks to develop…
We present an asymptotic result for the Laplace transform of the time integral of the geometric Brownian motion $F(\theta,T) = \mathbb{E}[e^{-\theta X_T}]$ with $X_T = \int_0^T e^{\sigma W_s + ( a - \frac12 \sigma^2)s} ds$, which is exact…
We solve the superhedging problem for European options in an illiquid extension of the Black-Scholes model, in which transactions have transient price impact and the costs and the strategies for hedging are affected by physical or cash…
In financial terms, an implied volatility surface can be described by its term structure, its skewness and its overall volatility level. We use a PCA variational auto-encoder model to perfectly represent these descriptors into a latent…
In this paper, we analyze the robustness and sensitivity of various continuous-time rough Volterra stochastic volatility models in relation to the process of market calibration. Model robustness is examined from two perspectives: the…
A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary…
Precisely forecasting the excess returns of an asset (e.g., Tesla stock) is beneficial to all investors. However, the unpredictability of market dynamics, influenced by human behaviors, makes this a challenging task. In prior research,…
We provide an European option pricing formula written in the form of an infinite series of Black Scholes type terms under double Levy jumps model, where both the interest rate and underlying price are driven by Levy process. The series…
Contingent Convertible bonds (CoCos) are debt instruments that convert into equity or are written down in times of distress. Existing pricing models assume conversion triggers based on market prices and on the assumption that markets can…
Trade prices of about 1000 New York Stock Exchange-listed stocks are studied at one-minute time resolution over the continuous five year period 2018--2022. For each stock, in dollar-volume-weighted transaction time, the discrepancy from a…
We present a method for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, which is based on a system of integral equations that relates terminal density and option prices. Using a discretization of…
In the Black-Scholes model, the absence of arbitrages imposes necessary constraints on the slope of the implied variance in terms of log-moneyness, asymptotically for large log-moneyness. The constraints are used for example in the SVI…
When trading American and Asian options in the FX derivatives market, banks must calculate prices using a complex mathematical model. It is often observed that different models produce varying prices for the same exotic option, which…
We show how to derive the Black-Scholes model and its generalisation to the `exchange-option' (to exchange one asset for another) via the continuum limit of the Binomial tree. No knowledge of stochastic calculus or partial differential…
Liquidations in Decentralized Finance (DeFi) are both a blessing and a curse -- whereas liquidations prevent lenders from capital loss, they simultaneously lead to liquidation spirals and system-wide failures. Since most lending and…
Transition risk can be defined as the business-risk related to the enactment of green policies, aimed at driving the society towards a sustainable and low-carbon economy. In particular, the value of certain firms' assets can be lower…