Alternatives to Classical Option Pricing
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Alternatives to Classical Option Pricing
“We develop two alternate approaches to arbitrage-free, market-complete, option pricing. The first approach requires no riskless asset. We develop the general framework for this approach and illustrate it with two specific examples. The second approach does use a riskless asset. However, by ensuring equality between real-world and risk-neutral price-change probabilities, the second approach enables the computation of risk-neutral option prices utilizing expectations under the natural world probability ℙ. This produces the same option prices as the classical approach in which prices are computed under the risk neutral measure ℚ. The second approach and the two specific examples of the first approach require the introduction of new, marketable asset types, specifically perpetual derivatives of a stock, and a stock whose cumulative return (rather than price) is deflated.”
Explanations.app
“Youtube style tutoring for competitive math”
Sega Saturn Architecture
“Welcome to the 3D era! Well… sorta. Sega enjoyed quite a success with the Mega Drive so there’s no reason to force developers to write 3D games right now.
Just in case developers want the extra dimension, Sega adapted some bits of the hardware to enable polygon drawing as well. Hopefully, the result didn’t get out of hand!”
Quantum Monte Carlo simulations for financial risk analytics
“Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios required for convergence. If a probability distribution is available, Quantum Amplitude Estimation (QAE) algorithms can provide a quadratic speed-up in measuring its properties as compared to their classical counterparts. Recent studies have explored the calculation of common risk measures and the optimisation of QAE algorithms by initialising the input quantum states with pre-computed probability distributions. If such distributions are not available in closed form, however, they need to be generated numerically, and the associated computational cost may limit the quantum advantage. In this paper, we bypass this challenge by incorporating scenario generation — i.e. simulation of the risk factor evolution over time to generate probability distributions — into the quantum computation; we refer to this process as Quantum MC (QMC) simulations. Specifically, we assemble quantum circuits that implement stochastic models for equity (geometric Brownian motion), interest rate (mean-reversion models), and credit (structural, reduced-form, and rating migration credit models) risk factors. We then integrate these models with QAE to provide end-to-end examples for both market and credit risk use cases.”
New concept for the value function of prospect theory
“In the prospect theory, the value function is typically concave for gains and convex for losses, with losses usually having a steeper slope than gains. The neural system largely differs from the loss and gains sides. Five new studies on neurons related to this issue have examined neuronal responses to losses, gains, and reference points. This study investigates a new concept of the value function. A value function with a neuronal cusp may show variations and behavior cusps with catastrophe where a trader closes one’s position.”