This paper shows how the prices of option contracts traded in financial marketscan be tracked sequentially by means of the Extended Kalman Filter algorithm. I consider call and put option pairs with identical strike price and time of maturity as a two output nonlinear system.The Black-Scholes approach popular in Finance literature andthe Radial Basis Functions neural network are used in modelling the nonlinear system generating these observations. I show how both these systems may be identified recursively using the EKF algorithm. I present results of simulations on some FTSE 100 Index options data and discuss the implications of viewing the pricing problem in this sequential manner. 1 INTRODUCTION Data from the financial markets has recently been of much interest to the neural computing community. The complexity of the underlying macroeconomic system and how traders react to the flow of information leads to highly nonlinear relationships betweenobservations.
Let's assume we know how much Tesla share costs in 2W. In other terms, if you are in two weeks time (i.e. in the future), what's the expected value of your portfolio, made of this one american option. You have information at 2W and you want to predict the option value at 1M. Beforehand, we need to simulate multiple scenarios for Tesla share price. For model simplicity, we suppose Tesla Share follows a Geometric Brownian motion path with mean r (risk free rate) and volatility Sigma 20% (we refer interested readers to Stochastic processes theory). NB: 1 month time is equivalent to about 0.08 year time.
We consider a popular problem in finance, option pricing, through the lens of an online learning game between Nature and an Investor. In the Black-Scholes option pricing model from 1973, the Investor can continuously hedge the risk of an option by trading the underlying asset, assuming that the asset's price fluctuates according to Geometric Brownian Motion (GBM). We consider a worst-case model, in which Nature chooses a sequence of price fluctuations under a cumulative quadratic volatility constraint, and the Investor can make a sequence of hedging decisions. Our main result is to show that the value of our proposed game, which is the regret'' of hedging strategy, converges to the Black-Scholes option price. We use significantly weaker assumptions than previous work---for instance, we allow large jumps in the asset price---and show that the Black-Scholes hedging strategy is near-optimal for the Investor even in this non-stochastic framework."
The Samsung Galaxy S9 is expected to pack some whole new features, more color options and a faster processor, which is why it's not going to be cheap. The upcoming flagship Android phone may be the most expensive phone in the Galaxy S line as it's rumored to cost around $100 more than the Galaxy S8.
Apple just announced the iPhone 7 and the iPhone 7 Plus earlier today, along with the Apple Watch Series 2. What the tech giant didn't tell the crowd at the Bill Graham Civic Auditorium in San Francisco is that it also updated its older iPad models and reduced the pricing for the iPad Pro, according to MacRumors. The minimum storage for the iPad Air 2, 3, iPad mini 4 and iPad mini 2 have all been increased from 16GB to 32GB. The 32GB version of the iPad Air 2 and iPad mini 4 sells for 399, while the 32GB Wi-Fi only version of the iPad mini 2 costs 269 and its Cellular model sells for 399. The iPad Air 2 and mini 4 now also have a 128GB capacity variant. However, the iPad mini 2, which is the oldest out of the bunch, will only have a 32GB model and nothing else.