We present an algorithm and its software implementation that computes implied volatilities for exchangetraded stock options. The LR (Leisen-Reimer) binomial tree is used for the underlying option pricing, which is adjusted for dollar cash dividends. The Brent’s method is used as the root-finding procedure. The option pricing procedure that is at the core of the root-finding is optimised to maxi...

A real option on a commodity is valued using an implied binomial tree (IBT) calibrated using commodity futures options prices. Estimating an IBT in the absence of spot options (the norm for commodities) allows real option models to be calibrated for the first time to market-implied probability distributions for commodity prices. Also, the existence of long-dated futures options means that good ...

An option is a nancial contract whose value depends on that of an underlying asset such as a company stock. The Black-Scholes model for option pricing, published in 1973, revolutionized the nancial industry by introducing a no-arbitrage paradigm for valuing uncertainty and hedging against risk. This simple model assumes that the underlying stock price follows a stochastic Brownian motion proces...

More than 60% of accidents in Iran occur within 30 kilometers of cities entrance roads. Therefore the number of accidents per kilometer in these regions, in contrast to the other parts of roads is very considerable. The city of Tehran, as the capital of Iran, is the cross point of major arterials of passenger and freight transportation. Thus the evaluation of road safety, entering and exiting t...

An edge-colored graph G is conflict-free connected if, between each pair of distinct vertices, there exists a path containing a color used on exactly one of its edges. The conflict-free connection number of a connected graph G, denoted by cfc(G), is defined as the smallest number of colors that are required in order to make G conflict-free connected. A coloring of vertices of a hypergraph H = (...

As the transition to renewable energy sources progresses, their integration makes electricity production increasingly fluctuating, also causing amplified volatility in electricity prices on energy markets. To contribute to power grid stability, utilities need to balance volatile supply through shifting demand. This measure of demand side management creates flexibility, being enabled as the inte...

In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are naturally derived from game-th...

The security dynamics described by the Black-Scholes equation with price-dependent variance can be approximated as a damped discrete-time hopping process on a recombining binomial tree. In a previous working paper, such a nonuniform tree was explicitly constructed in terms of the continuous-time variance. The present note outlines how the previous procedure could be extended to multifactor Blac...

We prove that the expectation of the binomial distribution of order k with success probability p is monotonically increasing with respect to p for all n and k. The result is extended to the problems on exchangeable random sequences and expectations of distributions of mixtures of binomial distributions of order k are studied. If the mixing measure is stochastically increasing with respect to it...

This research investigates how the price frame affects the consumer’s preference. Using qualitative methodology from the prospective of behavioral science, we find in the overall assessment of a product, the consumers have more selective attention and thus higher weight on secondary attributes under partitioned pricing than under combined pricing. That means in online selling, consumers pay mor...