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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18 views

Methods Available for Derivative Pricing in Mathematica? [closed]

I am using Mathematica to price options (built in functions, no need to reinvent the wheel, right?). In the documentation, the Binomial method is used as an example of specifying a non-standard ...
7
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4answers
691 views

Why does it take so many lines of code to price even the simplest of options with QuantLib

I have been looking at QuantLib I am trying to figure out why I need to write so much boilerplate code even when pricing the "simplest" of European Options using the analytical Black-Scholes formula ...
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1answer
123 views

Understanding skew of SPX - Why does IV of OTM puts increase with strike?

I've been trying to understand the skew I see when looking at the skew of SPX. Here is a snapshot today from thinkorswim. I understand why IV increases for ITM puts -- namely because there is a ...
5
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1answer
320 views

How to use a change of numeraire to price this option?

I recently asked this question regarding how to price an option with payoff: $$\text{Payoff}_T = (A_TR_T - A_T \lambda)^+ $$ Let's assume for generality that $A_t$ and $R_t$ are GMB's: $$dA_t = ...
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1answer
122 views

What is the correlation between these two functions of GBMs?

Let's say that I have two correlated GBMs: $$dA_t = A_t \sigma^A dW^A_t$$ $$dR_t = R_t \sigma^R dW^R_t$$ $$dW^R_t dW^A_t = \rho dt$$ I am trying to price a derivative which payoff at time $T$ is: ...
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0answers
202 views

Max option leverage strike

Since options represent leveraged stock investments, at which strike $K$ does a European option provide maximum leverage? Hereby define leverage $L$ as ratio of Delta/Optionprice: ...
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1answer
79 views

What is more likely effect to call and put prices, respectively, if the stock price decreases by$1?

The current stock price is \$80.Call ,and ,put, options, with ,exercise ,prices, of $50 and 3 days to maturity are currently trading. What is more likely effect to call and put prices, respectively, ...
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0answers
59 views

Logic between options and risk free rate [closed]

What is the relationship between put option price and risk free rate? And between call options price and risk free rate? Explain the logic? No calculation.
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0answers
22 views

Financial Derivative, European Option [closed]

Market Prices for European put and call options on ABC stock are as below: Call = $4.5 Put = $6.8 Exercise Price, X =$70 Risk Free Annual Compounded rate r = 5% Time to expiration T = 139 days ...
2
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0answers
31 views

Equity protection and butterfly certificates pricing

Certificates issued by famous industry names are usually made up by a combination of a fixed income instrument and some vanilla and exotic options. I am looking for something which explains: how to ...
1
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0answers
37 views

Gil-Palaez Inversion Formula in Black Scholes world

I am trying to calculate numerically the price of a plain vanilla call through Fourier Transform, by applying the Gil-Pelaez formula. More precisely, we have that C(K)=S0*Π1-Kexp(-rT)Π2 where ...
4
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1answer
141 views

At-the-money Call Spread approximation

In a trading manual I got during a course, the value of the ATM Call-Spread is approximated by $CS_{ATM}=\frac{1}{2}StrD+(F-m)\times\Delta CS$ The lecturer skipped the part where he derived this ...
4
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0answers
60 views

Are there academic papers on the 'term structure' of adverse selection for futures and options?

By term structure I mean a non-stationarity in the pattern of intraday adverse selection as a given instruments approaches its expiry. Note that I am interested in the adverse selection on the ...
4
votes
1answer
64 views

When are ES E-mini future options issued?

Since options lose 2/3 of their time value in the second half of their lifespan, it makes sense to be aware of when an option was issued. What are ways of figuring out when ES futures options have ...
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1answer
92 views

American put option and rising interest rate

Will a rise in interest rate always result in a lower price of an American put option?
4
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1answer
90 views

Forced to exercise gap options

I was reading a textbook and came across some surprising stuff in the section about gap options. Let $X$ be a payoff function such that $X=\Big\{\matrix{0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...
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9answers
6k views

Why Drifts are not in the Black Scholes Formula

This question has puzzled me for a while. We all know geometric brownian motions have drifts $\mu$: $dS / S = \mu dt + \sigma dW$ and different stocks have different drifts of $\mu$. Why would ...
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2answers
81 views

put call parity for futures options derivation in Hull

In Hull, the following derivation of PCP for futures options: What confuses me is that it is stated that the payoff of the long futures is $F_t-F_0$. The footnote states: the analysis assumes that ...
5
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2answers
232 views

Covariance structure of call option surface

Assume the observed call option prices $C(K_i,T_i)$ for $i = 1,\dots,N$ are disturbed by some unknown measurement noise $\epsilon$. What would an appropriate covariance structure be for $\epsilon$? ...
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1answer
60 views

Immunization: Whats the best way to hedge my short interest rate exposure?

What's the best way to hedge a portfolio against a rise in rates? Portfolio: long bonds different maturities. a) parallel shift b) convex shift (short and long term rise more than mid term) How is ...
1
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1answer
146 views

Numerical Solutions for PIDE

I want to solve an exotic options of PIDE by Numerical Methods.I just focus on the integral part of PIDE and want to underestand some tips on numerical solution of how to numerically solve it. Exactly ...
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3answers
9k views

What is a Heat Rate Option?

I tried a search with google but I can't find a clear definition of what a Heat Rate Option is. I would appreciate if someone could explain to me what this type of option is. My understanding is ...
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2answers
104 views

Why the value of this portfolio is negative? [closed]

Let's assume I buy 1 call with strike 100 and 1 call with strike 120 I sell 2 calls with strike 110 (with same expiration) I wonder why value of this portfolio is negative at $t=0$?
5
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1answer
337 views

Backtesting on historical option data

I have downloaded some daily historical option data for a timespan of 10 years and want to perform trading backtests with them. Data are European index options, on ODAX. My question is about realistic ...
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0answers
65 views

How big is the options market?

I am looking to write an intro to a document describing option pricing. Therefore it would be lovely to motivate it by how large the market is, but I cannot find any good reference. Where can I find ...
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6answers
1k views

Do binary options make any sense?

Reading from "www.nadex.com" - the copy reads "Binaries are similar to traditional options but with one key difference: their final settlement value will be 0 or 100. This means your maximum risk and ...
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0answers
74 views

Discrete Hedging of Options

Assume that a stock $S_t$ follows simple geometric Brownian motion. Let's say we sold option whose payoff is $f(S_T)$. Now, we are only allowed to trade 2 times in the interval [0,T]. What kind of ...
7
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1answer
1k views

Can American options with no dividends and zero risk-free rate be treated as European?

Let's say you've got American options on a future of a stock index. There are no dividends, and no risk-free rate either (assume $r=0$). Can these options then be treated as European from the ...
0
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1answer
48 views

In this scenario could gamma be higher for OTM options?

Let's say there is a $1 stock, with say 1 day to expiration. The 1.5 strike call, is probably a 0 delta at this point; however, a 1 point increase would mean the stock would be at trading at 2 ...
0
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1answer
58 views

What is the correlation of stock options?

I want to calculate the VaR of two correlated option positions, and I know the correlation between stock price returns. I want to separately calculate $Var_1$,$Var_2$ for option 1 and 2, and then use ...
0
votes
1answer
349 views

Gamma Imbalance Explanation

Can someone please give me an explanation as to what put-call gamma imbalance specifically refers to (imbalance of what?), and why they may exacerbate volatility from a market perspective, and why the ...
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1answer
61 views
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3answers
212 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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1answer
192 views

Feynman Kac Formula for path-dependent options

Consier geometric Brownian motion: $dS_t/S_t=\mu dt+\sigma dW_t$ Feynman Kac theorem tells us that the conditional expectation $v(t,x)=E[ e^{-rT}\Psi(S_T) | S_t=x]$ can be computed by solving the ...
0
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1answer
117 views

VIX Calculation - weighting of strikes

The formula for calculating the VIX from SPX options is given on page 4 of this document: https://www.cboe.com/micro/vix/vixwhite.pdf My question is, why is the option price at each strike weighted ...
0
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1answer
58 views

Interpretation of vega out of BS formula

I am comparing Monte Carlo estimates of VaR (using importance sampling) under both the normal and student distributions. I am also considering risk factors other than log-prices; in particular, ...
0
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1answer
80 views

What exotic options are exchange-traded?

There are a number of exchanges that trade vanilla Call/Put American/European options on various underlyings (equities, indices, futures). There have been some trading in digital options on certain ...
2
votes
1answer
293 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 ...
16
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3answers
4k views

Papers about backtesting option trading strategies

I am looking for all kinds of research concerning option trading strategies. With that I mean papers that publish results on different option trading strategies properly backtested with real-world ...
0
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1answer
76 views

Citable source: Why implied volatility over dollar prices

I am aware of the reasoning of quoting vanilla options as implied volatilities rather than dollar values. However, I would like to have a literature reference where this is explained, to quote / cite ...
0
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0answers
48 views

Risks Associated with Option Arbitrage Portfolio

If my math is correct, if I construct the following portfolio of options the worst that I can do regardless of what the underlying does is profit $1.74 (less commissions). Is this correct? Are there ...
1
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1answer
100 views

Option writing optimal sell time

When selling options, e.g. a straddle I read often the optimal time for selling options is 30-40 days until expiration. For me intuitively the optimal time would be around one week until expiration ...
1
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1answer
20 views

Where do Over-allotment (Greenshoe) option shares come from?

I'm just wondering, if following an IPO the share price goes up and the underwriter calls the option, where do those extra 15% shares come from? Does the company have to issue more stock to cover the ...
1
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3answers
102 views

Is it realistic to assume that the current price of a stock takes into account the probability of it going up or down in the future?

I'm currently reading the following lecture notes: http://www1.maths.leeds.ac.uk/~jitse/math2515/lecture04.pdf On the second page, under the subsection titled "The Risk-Neutral World" it points out ...
7
votes
6answers
14k views

How to calculate stock move probability based on option implied volatility and time to expiration? (Monte Carlo simulation)

I am looking for one line formula ideally in Excel to calculate stock move probability based on option implied volatility and time to expiration? I have already found a few complex samples which took ...
1
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2answers
137 views

Linear combination of geometric Brownian motion

Let $X_t= e^{\left(\mu-\sigma^2/2 \right)t+\sigma W_t}$ be a geometric Brownian motion with drift $\mu$ and volatility $\sigma$. I am trying to find an analytical solution to $$\mathbb{E}\left[ ...
3
votes
1answer
441 views

Option prices in Bates SVJ model?

In this [post] discussed the European put and call price formulas under the Heston Stochastic Volatility model. There exists an important extension of Heston model to include diffusion jumps, known ...
3
votes
2answers
150 views

How do I calculate the probability of a stock being above or below a value using the Heston model?

How can I use the Heston Model to calculate the probability of a stock being above or below a certain value on a given date in the future?
6
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1answer
714 views

Need historical prices of EUREX American and European style options

I am trying to get the historical price data on selected American and European style options at EUREX. I am not familiar with their system. Does any one know whether they have something like yahoo ...
4
votes
1answer
229 views

US options market/microstruture research

Can someone point out where to find up to date market/microstruture research in the options market?