|Gena Ioffe, Mark Ioffe, David Krell - Pricing of Binary Range and Double KO Options.|
This paper provides close form pricing formulas for double knock out and binary range options.
|Gena Ioffe - Differences in Theoretical and Actual Prices of Double Knock-out and Binary Range FX Options.|
In this paper, Ioffe:
- Described an approximation formula that is used by some market participants to price 2KO and Range options.
- Explained why and under which conditions this approximation formula will produce higher valuations than when using a model specifically designed for such purpose.
- Described several methods that may be useful to practitioners in static replication and hedging of 2KO and Range options.
- Provided an identity formula, that relates 2KOC and 2KOP to Range options. This identity formula may be used in a similar way as the Put/Call Parity.
|Mark Ioffe - Digital FX option arbitrage|
We found out a theoretical possibility to build arbitrage for FX options. This possibility based on drawback Black-Sholes model. As sample, we analyze digital option, but the same is true for other FX options. For practical decision we use FOCUS system
|Mark Ioffe - About a finite different method for pricing of Equity Lookback options.|
We try to clarify what “finite difference method” means in the financial literature. A finite difference method in mathematics is a numerical method for solving a partial differential equation (PDE). It seems that in the financial literature it is something different. We analyze this issue using as an example the pricing of Equity Lookback options.
|Mark Ioffe - Probability Distribution of Cox-Ingersoll-Ross Process|
The classical Cox-Ingersoll-Ross process is wide spread in theoretical finance literature. This process has the noncentral chi-square distribution. By solution of first order linear partial differential equation we calculated characteristic function of this process and compare it with known characteristic function of noncentral chi-square distribution. In general case this functions and distributions are different.
|Mark Ioffe - Using matlab for select applied problems.|
Matlab software is used for solving across a wide spectrum of applied problems and has a specific character. This article presents a basic mathematical formulas and Matlab functions for computer aided tomography, when the process of reconstructing an image from projection through the image is simulated.
|Mark Ioffe - Clique option pricing|
We show how can be calculated Clique option premium. If number of averaging dates enough great we use central limit theorem for stochastic variables and derived analytical formula for option price. For small number of averaging we use 2 methods: Monte Carlo and method based on Gauss Legendre formula for numerical integration.
|Mark Ioffe - Variance swaps pricing|
This article describes potential practical approaches to volatility swap pricing. We analyze 3 possible pricing methods based on historic data. First method used historic volatilities, second method uses implied volatilities and third method uses direct option prices.
|Mark Ioffe - American exchange option pricng|
We describe 3 potential methods for calculation American exchange option price. For European exchange option exists analytical formula for pricing (formula Margrabe). Unfortunately, there is no analytical formula for American option and we must use numerical method. We analyze 3 possible numerical methods. On our opinion, the best is Gauss-Hermite method of numerical integration.
|Mark Ioffe - Boost option pricing|
We describe method for pricing of BOOST option. Method based on solving of partial differential equation (PDE) by using Fourier transformation. We reduce pricing problem to numerical integration. For numerical integration we use Simpson’s method.
|Mark Ioffe - The Old VIX vs. New VIX|
In 1993, the Chicago Board Options Exchange® (CBOE®) introduced the CBOE Volatility Index® .VIX ® and it quickly became the benchmark for stock market volatility. The index calculations were based on paper by Professor Robert E. Whaley of Duke University. Accordingly this paper VIX ® is constructed from implied volatilities of the eight near–the-money, nearby, and second nearby OEX option series.