The paper reviews the option pricing model constructs of Bachelier and Black-Scholes Merton, concluding the latter model approximates the former. The paper demonstrates that certain critiques of the Bachelier model outlined in the 1960s and 1970s are not sound; and Bachelier's model can be...

The Black-Scholes framework implies a constant volatility across term and strike, and a lognormal distribution for underlying asset prices. However, it is known that empirical data violates this assumption. In this report we describe, motivate and apply a model-independent,...

We propose a new nonparametric technique to estimate the CALL function based on the superhedging principle. Our approach does not require absence of arbitrage and easily accommodates bid/ask spreads and other market imperfections. We prove some optimal statistical properties of our estimates. As...

In this paper, we derive closed-form, interpolation-based expressions for European call options written on defaultable assets. Our results are based on the work of Henderson at al. (2007), who derive formulas that incorporate standard static no-arbitrage restrictions, and Orosi (2014) who...

American options are actively traded worldwide on exchanges, thus making their accurate and efficient pricing an important problem. As most financial markets exhibit randomly varying volatility, in this paper we introduce an approximation of American option price under stochastic volatility...

In this paper, I have used simple arbitrage argument to derive a dozen of model-free option price properties. In addition to deriving the Greeks under the model-free framework, the results show that first, in contrast to the traditional view, a European call (put) option for a...

In this work, we adapt a Monte Carlo algorithm introduced by Broadie and Glasserman in 1997 to price a π-option. This method is based on the simulated price tree that comes from discretization and replication of possible trajectories of the underlying asset's price. As a result, this algorithm...

In this paper we present a critical point on connections between stock volatility, implied volatility, and local volatility. The essence of the Black Sholes pricing model is based on assumption that option piece is formed by no arbitrage portfolio. Such assumption effects the change of the real...

Under the recent negative interest rate situation, the Bachelier model has been attracting attention and adopted for evaluating the price of interest rate options. In this paper, we will derive an option pricing formula based on the Bachelier model and compare it with the prior researches. We...