An Interpolation-Based Approach to American Put Option Pricing

In this paper we provide alternative methods for pricing European and American call and put options. Our contribution lies in the simplification attempted in the models developed. Such simplification is feasible due to our observation that the value of the option can be derived as a function of the underlying stock price, strike price and time to maturity. This route is supported by the fact that both the risk-free rate and the volatility of the stock are captured by the move of the underlying stock price. Moreover, looking at the properties of the Brownian motion, widely used to map the move of the stock price, we realize that volatility is well depicted by time. Last but not the least, the value of an option is an increasing function of both time and volatility. We find simplified option pricing formulas depending on the underlying asset (price and strike price) and the time to maturity only. We test our formulas against the S&P 500 index options; the advantage of the approach is that less simplifying assumptions are needed and much simpler methods are produced. We provide alternative formulas for pricing European- and American-type options.

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“…The Black-Scholes model is a classical example of this phenomenon. Our view is echoed by Orosi (2015Orosi ( , 2017 and Alghalith (2014).…”

Section: Introductionmentioning

confidence: 78%

“…Finally, Orosi (2017) discusses the construction of interpolation-based models for American put options. He derives a closed-form expression and suggests multiparameter extensions.…”

Section: Introductionmentioning

confidence: 99%

Simplified Option Pricing Techniques

2019

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“…Assuming the absence of default, an analytic expression for American put options can be derived by following the framework presented in Orosi (2015). The main idea behind this approach is as follows.…”

Section: Methodsmentioning

confidence: 99%

“…We introduce a simple method for extracting the probability of a firm's default from the prices of American put options on the firm's stock. Building on the idea of a default corridor proposed by Carr and Wu (2011; hereafter, referred to as CW) and the option‐pricing method proposed by Orosi (2015), we first derive a new parsimonious closed‐form pricing formula for American put options, which incorporates the possibility of default. We then calibrate the parameters of the proposed pricing formula to the observed put option prices to obtain an estimate of the probability of default (PD).…”

Section: Introductionmentioning

confidence: 99%

A simple method for extracting the probability of default from American put option prices

Chang

Orosi

2020

Journal of Futures Markets

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We present a novel method for extracting the risk‐neutral probability of default (PD) of a firm from American put option prices. Building on the idea of a default corridor proposed by Carr and Wu, we derive a parsimonious closed‐form formula for American put option prices from which the PD can be inferred. The method is easy to implement. Our empirical results based on seven large US firms for the period 2002–2010 show that, in some cases, our option‐implied PD can provide a more accurate estimate of default probability than the estimates implied from credit default swaps.

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“…We introduce a simple method for extracting the probability of a …rm's default from the prices of American put options on the …rm's stock. Building on the idea of a default corridor proposed by Carr and Wu (2011) (hereafter, referred to as CW) and the option-pricing method proposed by Orosi (2015), we …rst derive a new parsimonious closed-form pricing formula for American put options, which incorporates the possibility of default. We then calibrate the parameters of the proposed pricing formula to the observed put option prices in order to obtain an estimate of the probability of default.…”

Section: Introductionmentioning

confidence: 99%

A Simple Method for Extracting the Probability of Default from American Put Option Prices

Chang

Orosi

2020

SSRN Journal

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Bank of Canada staff working papers provide a forum for staff to publish work-in-progress research independently from the Bank's Governing Council. This research may support or challenge prevailing policy orthodoxy. Therefore, the views expressed in this paper are solely those of the authors and may differ from official Bank of Canada views. No responsibility for them should be attributed to the Bank.

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An Interpolation-Based Approach to American Put Option Pricing

Cited by 4 publications

References 14 publications

Simplified Option Pricing Techniques

Simplified Option Pricing Techniques

A simple method for extracting the probability of default from American put option prices

A Simple Method for Extracting the Probability of Default from American Put Option Prices

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