A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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2k views

Delta Neutral / Gamma Neutral Positions

I've been trying to find out more about options positions which are both delta neutral and gamma neutral--created with some kind of calendar spread. Supposedly, such a trade will be perfectly hedged ...
2
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2answers
166 views

Time-zero price of two specific contingent claims

I am unsure how to start with the following problem. I have two contingent claims where contingent claim (1) pays $\int_0^T S_u du$ and contingent claim (2) pays $(\log S_T)^2$ at time $T$ Now I ...
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2answers
1k views

Finding Probabilities Using The Binomial Model

I was not able to find a similar question when searching, but if I've missed one please feel free to point me to it. Unfortunately the closest example in the textbook was not terribly helpful either. ...
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2answers
726 views

Index arbitrage with Options when not all underlyings have options listed?

One arbitrage strategy involves looking at the price of the Index Futures price compared with the prices of the options contracts for the underlyings. My question is, can this arbitrage strategy ...
2
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1answer
161 views

Question on OptionMetrics: when are adjustments for discrete dividends needed?

Bakshi et. al. (1997) analyzes the empirical performance of some alternative option pricing models. I am interested to do this as well - hence applying different models - but I am unsure how to handle ...
2
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1answer
225 views

Why is this delta-hedging/P&L example on a variance swap call correct?

I'm looking into this article about var swaps: http://sbossu.com/docs/VarSwaps.pdf and not sure how to correctly interpret Exhibit 2.1.1. "In this example an option trader sold a 1-year call ...
2
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1answer
82 views

When $C(K_2) = C(K_1)$ for call options with the same expiration date

The exercise is to show $C(K_1) \geq C(K_2)$ where C(K) denotes the value of a call option on a stock price S with strike price K. We assume the expiry is the same for both. I have proved this by ...
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1answer
106 views

How literature come up with risk-neutrality problem, considering that market is not really risk-neutral?

I am searching on real-option pricing deficiencies to encounter risk-neutrality. As we know risk-neutrality assumption, is not hold in real situations. The problem is that I could not classified ...
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3answers
238 views

What noun is used to describe whether an option is call or put?

I'm not sure if this should be asked elsewhere, but it seems like a good place as any. Options have a strike price, they have an underlying instrument, and they have an expiry. They are also either ...
2
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1answer
232 views

Call option on a Mutual Fund

I am trying to price a call option on a mutual fund. Given the lack of market implied data, I am going to estimate the fund´s expected volatility using as a reference its historical volatility ...
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3answers
214 views

Why are short expiries associated with more pronounced volatility skews?

I've noticed that for a given strike price, the shorter expiration dates of options have more pronounced volatilities why is that?
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1answer
787 views

How to replicate this option?

I have a question I am not sure how to approach: Suppose interest rates is 50%, a stock worth \$1 today can be worth \$2, \$1, \$0.5 next year. If the option that pays \$1 only when S = \$2 is ...
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2answers
238 views

What is most reasonable approach to determine side of a multi-leg options order?

Say, 4-legged multi-leg options order with below leg ...
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2answers
425 views

Hedging credit risk using Put equity options

I am looking for some paper or similar which deal with this topic: hedging bankruptcy on firm's debt using Put options written on that firm's equity price. This should be based on the assumption that ...
2
votes
1answer
433 views

Calculating the probability of a price change using an options pricing formula

I don't know if I'm doing this right and I'd greatly appreciate help. I'm trying to use an option pricing formula to backout the likelihood of the Euro dropping below $1.27, even for a minute, at any ...
2
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1answer
230 views

Greeks and Option Premium

If a linear sum of options is constructed such that the premium payout is zero, then does it mean that resultant greeks of the cumulated options positions will be nearly zero. For simplicity, lets ...
2
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2answers
143 views

Buying one company or index against another, is this readily possible with options, with an accurate return (also Alpha Indexes)

There's a relatively new product in the market / on the Nasdaq called Alpha Indexes. It lets one own a company -- e.g. Apple, GE, Google, etc -- as the difference between how that company does (the ...
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1answer
64 views

Implied Volatility in Heston Model

recently I started reading the interesting book about option pricing in the stochastic volatility world from Lewis. He gives very interesting and detailed insights about this topic in general. However ...
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3answers
69 views

How would I exploit arbitrage if risk-neutral pricing doesn't hold? (Option Pricing)

We are just learning about binomial option pricing, and how the up-factor and the down-factor must match the risk-neutral price. p * u + (1 - p) * d = continuous risk free rate compounded CRR ...
2
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3answers
188 views

Why can't you arb skew by buying options with low implied vol and selling high implied vol in the same month and dynamically hedging?

there's something I've been trying to understand for a while now and I just can't quite understand with regards to skew. In the same month, why can't you buy a option that have low implied vol on the ...
2
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2answers
85 views

Hedging portfolio and extraction PDE of SV model with stochastic interest rate

How can I extraction this PDE \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + \frac{1}{2}P_{\sigma ...
2
votes
1answer
120 views

How to hedge a put under the Black-Scholes model?

To hedge a call, one would invest the option price proceeds into $\Delta_t*S_t + B_t = c_t$. (ok) However, a put has negative delta, so I would short $\Delta_t*S_t$ and invest ...
2
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1answer
81 views

Pricing digital options in discrete time

I am stuck in this exercise from my textbook: Consider a one-period market model with $N+1$ assets: a bond, a stock and $N-1$ call options. The prices of the bond are $B_0=1$ and $B_1 = 1+r$, ...
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2answers
113 views

Braess's paradox in quantitative finance: When optionality leads to lower value…?

One of the standard tenets of quantitative finance is that options should have an intrinsic value because optionality as such (in the sense of having more choices) should bring about value. This ...
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3answers
415 views

Any New Discoveries in Quantitative Finance?

It seems like the field has become stagnant in the decades following the enormously successful and influential Black Scholes model. (The original paper has been cited a staggering 25,000 times - more ...
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1answer
226 views

Some questions about implied volatilities and how to generate theoretical prices when market prices are not available

I am building a little Excel file that take some option prices in input and plots the volatility smile/surface. I have a script that reads market prices from the option chain for 3 different ...
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2answers
340 views

How to compute the VaR for European Call, using the delta-normal method?

I have a European call option with current stock price $S_0$, strike $K$, risk-free rate $r$, volatility $\sigma$, and time to maturity $T$ years. I assume that the stock price at time $t$, which is ...
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1answer
788 views

Effect of time to maturity on european put option

Let $C(K,T,S_0)$ denote the price of an European call option with strike K and maturity T on underlying price $S_0$. Assume interest rate $r>0$. Then of course $C(K,T,S_0) \geq 0$ and $C(K,T,S_0) ...
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1answer
135 views

Asymptotic behavior of theta of vanilla call option

It is well known that the theta of call option is always negative. Also, the theta of (at the money call option) goes to infinity as the time approaches to the maturity. On the other hands, (ITM and ...
2
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1answer
613 views

How does Volatility Pairs Trading work?

I've read some material related to pairs trading for equities and I understand the process of finding non-stationary pairs price series that can be cointegrated to form a stationary series. The basic ...
2
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2answers
205 views

what is the actual point of vega on real option data

For a call option, we know that the vega is the derivative of the price wrt to the volatility. However the volatility, in that context, actually refers to the implied volatility of the specific call ...
2
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1answer
158 views

QuantLibXL - Optionlet bootstrapping failure

I am trying to bootstrap the Optionlet volatility surface from a Cap/Floor volatility surface using QuantLibXL. To be specific, the data is from ICAP: ...
2
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1answer
522 views

Implied probability density (Question 2 - Applications and Interpretation)

Using the second derivative of the Call-Option-Price one can try to recover the pricing density. Formally: Assuming a constant interst rate $r$ and also not making any assumptions on the model ...
2
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1answer
669 views

Aprox intraday implied volatility using intraday option prices and EOD greeks

I have two options datasets: EOD IV and Greeks Tick option and underlying prices I'm looking to calculate IV for each tick. Is there a way to approximate the ticks' IV using last EOD Greeks and ...
2
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1answer
150 views

Hedging differences between equity and index options?

Suppose we hedge an index option using futures on that index. How would the hedging strategy be different if the underlying could be traded directly (from a risk point of view)?
2
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1answer
160 views

OTC Equity Options' Dynamics

This only applies to options that do not have marketable equivalents since margin can be marked to them. I've never been able to find this on my goog. How is margin typically calculated for OTC ...
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2answers
1k views

How to calculate Vomma of Black Scholes model

This source (PDF) gives the closed-form for vomma (or volga, i.e. the second derivative of price w.r.t. volatility) of the Black Scholes option pricing model as: ...
2
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1answer
441 views

Is there any evidence that an option delta approximates ITM expiry probability?

Several sources (online and offline) that discuss the delta of a listed vanilla option, state that its delta is a (guesstimate?) of the probability of said option expiring ITM (in the BSM framework). ...
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2answers
481 views

Why don't options traders use charts? Or do they?

Retail trading platforms typically offer equity charts but only instantaneous quotes on options. It seems like even a few minutes of historical data would be useful when entering an order. Are charts ...
2
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1answer
880 views

What exactly is the annualized forward premium?

A forward contract has a premium of $ 0$ because it is an obligation to buy or sell something in the future (hence there is more risk). Call and put options, on the other hand, have premiums of $C$ ...
2
votes
1answer
71 views

Option analysis

Assume zero dividend and that the strike price for a European call option on a stock at a fixed maturity T and strike price K is given by C(K).Suppose that $C(K)=e^{-k}$ for all $K\geq 0$ ,then, I ...
2
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3answers
98 views

Greeks for binary option?

How to derive an analytic formula of greeks for binary option? We know a vanilla option can be constructed by an asset-or-nothing call and a cash-or-nothing call, does that help us? Wikipedia states ...
2
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1answer
107 views

What should be the sign of greek letter $\rho$?

I'm reading the book Risk Management and Shareholders Value in Banking by Resti & Sironi. I quote a paragraph from the book (Chapter 5, appendix): The derivative of an option’s value with ...
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2answers
176 views

European call down and out option (geometric Brownian motion, Monte Carlo, Euler)

I need to estimate the expected value and the Greeks of an European call down and out option, assuming geometrical Brownian motion of the asset, with Monte Carlo simulation employing Euler ...
2
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2answers
129 views

VaR calculation methods of options

I am a little bit confused about VaR in Options and I need a clarification for. I collected the following formulas, can you suggest what is the best formula and explain me why, please?
2
votes
1answer
297 views

Using FX ATM/RR/BF Volatility to Estimate Smile

Suppose $S$ is some FX rate, EUR/USD say, and $\sigma_{S}(K,T)$ is the implied volatility for some option written on $S$, sourced from the surface $\sigma_{S}(\cdot,\cdot)$ (alternatively, consider ...
2
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1answer
76 views

Black Scholes Model and Dividends

My question can be summarised as such: Consider a portfolio. Say it has a price $\Pi = x$. Portfolio consists of a stock and a sequence of call options underlying on the stock. It has been announced ...
2
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1answer
62 views

Solving a Non-Linear PDE using a Finite Difference Scheme

I have the following non-linear PDE and I have no idea how to go about solving it using a finite difference scheme in Python. Can someone get me started and/or point me to an algorithm for doing this? ...
2
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2answers
146 views

asian option – exotic option – real data, authentic examples?

I would be pleased if any of You can give me the real example of an asian option (or other exotic option) that is being traded or that is offered by some institution. I have been searching the whole ...
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2answers
408 views

How to break down an FX option P&L?

I am comparing the mark-to-market (MtM) valuations of two risk systems, with respect to FX Options. My question is can I quantify the difference in MtM given the following: System1 AUD/JPY, MTM = ...