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Exchange-Traded Barrier Option and VPIN: Evidence from Hong Kong
Exchange-Traded Barrier Option and VPIN: Evidence from Hong Kong

... A bull contract is similar to a call warrant with underlying stock price S, maturity date T, strike price X and barrier H, where S > H ≥ X. If the contract is not called back before time T, it matures with a payoff of ST – X. ...
Chapter XV (pdf format)
Chapter XV (pdf format)

... Eurodeposits. The most popular instrument in this market is the certificate of deposit (CD), which is a negotiable and often bearer instrument. We also mentioned that for long-term CDs (up to ten years), there is the possibility of selecting a CD with floating-rate coupons. For CDs with floating-rat ...
CFRM 546 - 0404
CFRM 546 - 0404

Risk and Risk Aversion
Risk and Risk Aversion

... In this margin transaction, the amount of your own money relative to the total position is called the percentage margin. The current legal limit on initial margin is 50%. At least 50% of the total position must be your own (unborrowed) money. There is also something called the maintenance margin, wh ...
The pricing of volatility risk across asset classes
The pricing of volatility risk across asset classes

paper - Kellogg School of Management
paper - Kellogg School of Management

... Fourier series and ordinary differential equations. The double-jump model presumes rare jumps, e.g., compound Poisson process, for both asset prices and their variances. It has been applied empirically by Broadie et al. (2007), Chernov et al. (2003), Eraker et al. (2003), Eraker (2004) among others ...
Solution
Solution

Managerial incentives to take asset risk
Managerial incentives to take asset risk

... Volatility Vega and total Asset Delta. Similarly, the Equity Incentive Ratio is the ratio of total Equity Volatility Vega and total Equity Delta. This basic analysis yields four results. First, the Asset Incentive Ratio suggests significant asset risk-taking incentives even when a CEO is compensated ...
PDF
PDF

... and wheat futures, and concludes that the seasonal components for all three commodities peak about two to three months before the beginning of harvest. For the literature on how fundamentals affect volatility, it has been established that volatility is time-varying (Koekebakker and Lien 2004), high ...
Document
Document

Introduction - Drake University
Introduction - Drake University

... Operational Advantages – generally derivative markets have lower transaction costs and greater liquidity compared to the spot market. Additionally they allow easier short sales helping to “complete” the market. Market Efficiency - Spot market prices are sometimes not consistent with assets true econ ...
Margins - ASX Clear - Australian Securities Exchange
Margins - ASX Clear - Australian Securities Exchange

Chapter 13 Answers
Chapter 13 Answers

... Even though we are solving for the  and expected return of a portfolio of one stock and the risk-free asset for different portfolio weights, we are really solving for the SML. Any combination of this stock, and the risk-free asset will fall on the SML. For that matter, a portfolio of any stock and ...
Option Spread and Combination Trading
Option Spread and Combination Trading

... options markets are the most heavily traded short-term interest rate futures and options markets respectively in the world. Like some other executing brokers, Bear Brokerage regularly stations an observer at the periphery of the Eurodollar option and futures pits with instructions to record all opt ...
"Leverage Effect" a Leverage Effect?
"Leverage Effect" a Leverage Effect?

... leverage seems to die out over a few months; and there is no apparent effect on volatility when leverage changes because of a change in outstanding debt or shares, only when stock prices change. In short, our evidence suggests that the "leverage effect" is really a "down market effect" that may have ...
Prescription pricing
Prescription pricing

The Equilibrium Term Structure of Equity and Interest Rates
The Equilibrium Term Structure of Equity and Interest Rates

... growth process in an otherwise standard long-run risks model à la Bansal and Yaron (2004) to generate the downward sloping term structure of equity risk premia. However, unlike Belo et al. (2015), we generate an upward-sloping term structure of (real and nominal) bond risk premia at the same time. ...
Chapter 2: More on the `Bad News Principle`
Chapter 2: More on the `Bad News Principle`

... Suppose that the current profit is Pi. The standard N.P.V. rule tells us that the policy “enter now” is better than the policy “never enter” if V(Pi)-I>0. However, other policies are possible too, including the policy “enter when the profit is Pi+1 or above it”. The value of this policy when the cur ...
Using Mean Reversion Skew andJoint Measure
Using Mean Reversion Skew andJoint Measure

Absence of Common Knowledge as A Source of
Absence of Common Knowledge as A Source of

Preview - American Economic Association
Preview - American Economic Association

Optimal strategies of hedging portfolio of unit
Optimal strategies of hedging portfolio of unit

OBS Risk - Drake University
OBS Risk - Drake University

... ln( S )  (r  s )t X ...
What Ties Return Volatilities to Price Valuations and
What Ties Return Volatilities to Price Valuations and

Stock prices volatility and trading volume
Stock prices volatility and trading volume

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Black–Scholes model

The Black–Scholes /ˌblæk ˈʃoʊlz/ or Black–Scholes–Merton model is a mathematical model of a financial market containing derivative investment instruments. From the model, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options. The formula led to a boom in options trading and legitimised scientifically the activities of the Chicago Board Options Exchange and other options markets around the world. lt is widely used, although often with adjustments and corrections, by options market participants. Many empirical tests have shown that the Black–Scholes price is ""fairly close"" to the observed prices, although there are well-known discrepancies such as the ""option smile"".The Black–Scholes model was first published by Fischer Black and Myron Scholes in their 1973 paper, ""The Pricing of Options and Corporate Liabilities"", published in the Journal of Political Economy. They derived a partial differential equation, now called the Black–Scholes equation, which estimates the price of the option over time. The key idea behind the model is to hedge the option by buying and selling the underlying asset in just the right way and, as a consequence, to eliminate risk. This type of hedging is called delta hedging and is the basis of more complicated hedging strategies such as those engaged in by investment banks and hedge funds.Robert C. Merton was the first to publish a paper expanding the mathematical understanding of the options pricing model, and coined the term ""Black–Scholes options pricing model"". Merton and Scholes received the 1997 Nobel Memorial Prize in Economic Sciences for their work. Though ineligible for the prize because of his death in 1995, Black was mentioned as a contributor by the Swedish Academy.The model's assumptions have been relaxed and generalized in many directions, leading to a plethora of models that are currently used in derivative pricing and risk management. It is the insights of the model, as exemplified in the Black-Scholes formula, that are frequently used by market participants, as distinguished from the actual prices. These insights include no-arbitrage bounds and risk-neutral pricing. The Black-Scholes equation, a partial differential equation that governs the price of the option, is also important as it enables pricing when an explicit formula is not possible.The Black–Scholes formula has only one parameter that cannot be observed in the market: the average future volatility of the underlying asset. Since the formula is increasing in this parameter, it can be inverted to produce a ""volatility surface"" that is then used to calibrate other models, e.g. for OTC derivatives.
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