Papers by Nikhil Jaisinghani
Social Science Research Network, 2024
Research Square (Research Square), Dec 12, 2023
This paper proposes a framework which is compliant with complex real-world market characteristics... more This paper proposes a framework which is compliant with complex real-world market characteristics for constructing subspaces within which lie investors compelled to take long positions, take short positions, or stand on the sidelines. To begin, I outline the relevant complex elements of securities markets. First, it is proposed that the market is not homogenous; the market is made up of many independent investors, each with their unique perspectives, forecasts, and levels of conviction. Second, it is proposed that investors are not risk neutral and have non-linear utility functions; the paper borrows an established utility function from behavioral finance. Third, it is shown that most market participants find an asset's price too high to buy and too low to short; an effective asset pricing framework must acknowledge this. Fourth, it is proposed that options prices better reflect the sentiment of those who do not invest than they reflect the sentiment of those who do invest. The framework can use a single option price to create short put and long put frontier curves which carve up the two-dimensional investor space (x=expected value of underlying at expiration, y=uncertainty of this expected value) into three subspacesinvestor buys, investor sells, and investor does nothing. When incorporating prices of multiple options on the same underlying asset with the same expiration date, the paper shows Dissecting the Investor Space into Long, Short, and Sideline Subspaces 3 that the price curves intersect at a "knot"; the short put knot and long put frontier curves narrow in on the median investor's expected return of the underlying asset.
Social Science Research Network, 2023
Many attempts have been made to estimate market characteristics from options prices, none more we... more Many attempts have been made to estimate market characteristics from options prices, none more well known than the Black Scholes model. Yet, no options pricing model is without significant criticism. And none are consistent with the characteristics of the market discussed in this paper. Prior to developing a pricing model, it is important to delve deep into the market that is to be modeled. It is the author’s belief that important characteristics of securities markets and how securities are priced are ignored by many pricing models. In particular, these often-ignored characteristics of securities markets that this paper emphasizes are: 1. Securities markets are not homogenous; investors have different perspectives. 2. Investors are risk averse. 3. Most investors sit on the sidelines, choosing not to invest in a particular asset; as a result, assets are priced by outliers in the market, not investors that are representative of the market. 4. Options prices are set by investors with different objectives; options prices tell us less about those who do invest than they do about those who do not invest. This paper attempts to make a compelling case that each of these market characteristics is true and relevant. The paper concludes that analysts pricing securities in general, and options models in particular, may achieve deeper insights by understanding not why an investor bought or wrote an option at a particular price, but why that price does not align with the utility function of most investors.
Social Science Research Network, 2022
This paper proposes a new option pricing model which can aid in our understanding of the distribu... more This paper proposes a new option pricing model which can aid in our understanding of the distribution of market participants. First, it is proposed that the market is not homogenous; the market is made up of many independent investors, each with their unique perspectives, forecasts, and uncertainties. Second, it is shown that most market participants find an asset’s price too high to buy and too low to short; an effective asset pricing model must acknowledge this. Third, it is proposed that investors are not risk neutral and have non-linear utility functions; the paper borrows an established utility function from behavioral finance. The model can use a single put price to divide the two-dimensional investor space (x=expected value of underlying at expiration, y=uncertainty of this expected value) into three areas – investor buys, investor sells, and investor does nothing. The model is proposed as a foundation which in time may be able to solve for the market’s mean future expected price of the asset and the market’s mean uncertainty of this price.
Social Science Research Network, 2022
In 1973, Fischer Black and Myron Scholes published their seminal work on options pricing. Their m... more In 1973, Fischer Black and Myron Scholes published their seminal work on options pricing. Their model relied on a clever hedge which seemingly resulted in a risk-free portfolio. However, further analysis of this portfolio reveals that it may not be risk-free at all. A truly risk-free portfolio must be risk-free with respect to incremental changes to all variables on which the portfolio's value is dependent. However, the Black Scholes hedged portfolio is only risk-free in one dimensionchanges in the underlying stock value. In particular, the hedged portfolio may not be riskfree with incremental changes in time. The conclusion that this portfolio is risk-free is questioned, and with it the Black-Scholes pricing model which is dependent on the risk-free nature of this "hedged" portfolio.
Calculations of option risk premia as per the formulas described in the paper "Extracting Op... more Calculations of option risk premia as per the formulas described in the paper "Extracting Option Risk Premia and Implied Expected Return from Option Prices"
SSRN Electronic Journal
Many attempts have been made to estimate market characteristics from options prices, none more we... more Many attempts have been made to estimate market characteristics from options prices, none more well known than the Black Scholes model. Yet, no options pricing model is without significant criticism. And none are consistent with the characteristics of the market discussed in this paper.
Prior to developing a pricing model, it is important to delve deep into the market that is to be modeled. It is the author’s belief that important characteristics of securities markets and how securities are priced are ignored by many pricing models. In particular, these often-ignored characteristics of securities markets that this paper emphasizes are:
1. Securities markets are not homogenous; investors have different perspectives.
2. Investors are risk averse.
3. Most investors sit on the sidelines, choosing not to invest in a particular asset; as a result, assets are priced by outliers in the market, not investors that are representative of the market.
4. Options prices are set by investors with different objectives; options prices tell us less about those who do invest than they do about those who do not invest.
This paper attempts to make a compelling case that each of these market characteristics is true and relevant. The paper concludes that analysts pricing securities in general, and options models in particular, may achieve deeper insights by understanding not why an investor bought or wrote an option at a particular price, but why that price does not align with the utility function of most investors.
SSRN Electronic Journal, 2021
This paper proposes a new method for extracting the market’s expected return of a stock from opti... more This paper proposes a new method for extracting the market’s expected return of a stock from options prices while also calculating option-specific risk discounts (calls) and premiums (puts). However, first, I revisit the variable μ (expected return of a stock) as it relates to stock prices in the Black-Scholes formula derivation. I postulate that μ is itself a function of time and therefore the partial derivative equation Black, Scholes, and Merton solved was incomplete. Importantly, this undermines the conclusion Black, Scholes, and Merton came to, that an option’s price is not a function of the expected return of the underlying stock. To extract the expected return from options prices, I begin by proposing formulas for call and put prices introducing variables for strike price specific discounts and premiums. Known qualities of options, required to satisfy the no arbitrage assumption, are then used to solve for these discounts and premiums as a function of the implied expected price of a stock and σ. Finally, implied expected price and σ are solved for using numerical analysis.
Journal of Insurance and Financial Management, 2022
In 1973, Fischer Black and Myron Scholes published their seminal work on options pricing. Their m... more In 1973, Fischer Black and Myron Scholes published their seminal work on options pricing. Their model relied on a clever hedge which seemingly resulted in a risk-free portfolio. However, further analysis of this portfolio reveals that it may not be risk-free at all. A truly risk-free portfolio must be risk-free with respect to incremental changes to all variables on which the portfolio's value is dependent. However, the Black Scholes hedged portfolio is only risk-free in one dimensionchanges in the underlying stock value. In particular, the hedged portfolio may not be riskfree with incremental changes in time. The conclusion that this portfolio is risk-free is questioned, and with it the Black-Scholes pricing model which is dependent on the risk-free nature of this "hedged" portfolio.
SSRN Electronic Journal
This paper proposes a new option pricing model which can aid in our understanding of the distribu... more This paper proposes a new option pricing model which can aid in our understanding of the distribution of market participants. First, it is proposed that the market is not homogenous; the market is made up of many independent investors, each with their unique perspectives, forecasts, and uncertainties. Second, it is shown that most market participants find an asset’s price too high to buy and too low to short; an effective asset pricing model must acknowledge this. Third, it is proposed that investors are not risk neutral and have non-linear utility functions; the paper borrows an established utility function from behavioral finance. The model can use a single put price to divide the two-dimensional investor space (x=expected value of underlying at expiration, y=uncertainty of this expected value) into three areas – investor buys, investor sells, and investor does nothing. The model is proposed as a foundation which in time may be able to solve for the market’s mean future expected price of the asset and the market’s mean uncertainty of this price.
(UC) and is charged with conducting unclassified research across a wide range of scientific disci... more (UC) and is charged with conducting unclassified research across a wide range of scientific disciplines.
Journal of Insurance and Financial Management, 2022
In 1973, Fischer Black and Myron Scholes published their seminal work on options pricing. Their m... more In 1973, Fischer Black and Myron Scholes published their seminal work on options pricing. Their model relied on a clever hedge which seemingly resulted in a risk-free portfolio. However, further analysis of this portfolio reveals that it may not be risk-free at all. A truly risk-free portfolio must be risk-free with respect to incremental changes to all variables on which the portfolio's value is dependent. However, the Black Scholes hedged portfolio is only risk-free in one dimensionchanges in the underlying stock value. In particular, the hedged portfolio may not be riskfree with incremental changes in time. The conclusion that this portfolio is risk-free is questioned, and with it the Black-Scholes pricing model which is dependent on the risk-free nature of this "hedged" portfolio.
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Papers by Nikhil Jaisinghani
Prior to developing a pricing model, it is important to delve deep into the market that is to be modeled. It is the author’s belief that important characteristics of securities markets and how securities are priced are ignored by many pricing models. In particular, these often-ignored characteristics of securities markets that this paper emphasizes are:
1. Securities markets are not homogenous; investors have different perspectives.
2. Investors are risk averse.
3. Most investors sit on the sidelines, choosing not to invest in a particular asset; as a result, assets are priced by outliers in the market, not investors that are representative of the market.
4. Options prices are set by investors with different objectives; options prices tell us less about those who do invest than they do about those who do not invest.
This paper attempts to make a compelling case that each of these market characteristics is true and relevant. The paper concludes that analysts pricing securities in general, and options models in particular, may achieve deeper insights by understanding not why an investor bought or wrote an option at a particular price, but why that price does not align with the utility function of most investors.
Prior to developing a pricing model, it is important to delve deep into the market that is to be modeled. It is the author’s belief that important characteristics of securities markets and how securities are priced are ignored by many pricing models. In particular, these often-ignored characteristics of securities markets that this paper emphasizes are:
1. Securities markets are not homogenous; investors have different perspectives.
2. Investors are risk averse.
3. Most investors sit on the sidelines, choosing not to invest in a particular asset; as a result, assets are priced by outliers in the market, not investors that are representative of the market.
4. Options prices are set by investors with different objectives; options prices tell us less about those who do invest than they do about those who do not invest.
This paper attempts to make a compelling case that each of these market characteristics is true and relevant. The paper concludes that analysts pricing securities in general, and options models in particular, may achieve deeper insights by understanding not why an investor bought or wrote an option at a particular price, but why that price does not align with the utility function of most investors.