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Questions tagged [options]

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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1answer
69 views

To use daily volatility or annual volatility

From Joshi's Quant Interviews books: The statistics department from our tell you that the stock price has followed a mean reversion process for the last 10 years, with annual volatility 10% and ...
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1answer
46 views

Quantlib specify contract duration instead of dates

I use the following code in Python to price American put/call options. It's simple code since I'm new to using Quantlib. I would like to specify the contract duration (i.e. ...
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1answer
112 views

What's the point of having an accurate option pricing model?

Just curious what's the actual reason of having an accurate option pricing model? For e.g. an option pricing model fits the volatility surface incredibly well, then what? Do practitioners actually use ...
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1answer
63 views

Greeks, European puts

I'm trying to solve this question but i have a lot of problems with it. European puts with maturity 6 months are written on an asset with current price $S_0=150.$ The annual interest rate is $r=16\%$ ...
2
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1answer
71 views

Risk Neutral Pricing and the Drift

For risk neutral pricing, why do we want to compute expectation of a martingale? why is this so important? Why do we dislike the drift so much? Avoid math heavy answers please.
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2answers
68 views

Deltas on Barrier options vs Vanilla options

In "Heard on the Street" it states that $$\Delta_{\text{up and out call}} \leq \Delta_{\text{standard call}} \leq \Delta_{\text{down and out call}}$$ Is there an intuitive explanation for why this ...
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3answers
51 views

Formula for the discounted payoff of a digital option

In "Heard on the Street" it states that the expected discounted payoff of a digital option is $$H\exp^{-r(T-t)}N(d_2)$$ where $H$ is the payoff of the option, the exponential is the discounting. ...
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1answer
66 views

Adjusting your delta hedge when the stock crashes and were originally delta hedged

You are long a call option on a stock and you are delta hedged. The stock crashes in price. How do you adjust your delta, do you buy or sell stock? Could answers please be quantitative (i am getting ...
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1answer
97 views

Proof that adding some quantity of stocks in a portfolio of option does not change the portfolio Gamma

I would like to proof mathematically and intuitively that adding some quantity of underlying to a portfolio of option does not change the overall gamma. Can you help me?
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1answer
55 views

Calculating Delta of option portfolio using average of inputs

Trying to think through two options portfolio scenarios, which are highly similar. I'm wondering if you can take a portfolio of options, all written against the same underlying product, and use ...
1
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0answers
55 views

Calculate upper bound for put option prices?

I need to know historical option prices for backtesting. The problem is I don't have such historical data. Is there a way to calculate the upper bound for out of money (American) put option selling ...
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0answers
47 views

Approximate Asian option price under Heston Model

I am looking to see if there is a formula or a derivation at least of an approximation of an Asian (Average Price) option under the heston model of stochastic volatility. Please advise
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1answer
75 views

Construction of Butterfly Spread as sum of Call Options

I have rigorously stated my problem here. The task at hand is to express a butterfly spread [no transaction fees] as a sum of long and short call options. I have found the solution on Wikipedia: $$\...
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1answer
43 views

Differences in bull put spread option strategy

I am supposed to construct a profit and loss diagram for a bullish spread strategy: −1put($X_{1}$) + 1put($X_{2}$) and compare it to the profit and loss diagram for the strategy: −10put ($X_{1}$)+ ...
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0answers
25 views

What is the effect of put call open Interest on price action

how option put call open Interest affects price actions as put sellers feel price when price goes down or call sellers feel pain when price goes up and how this affects price action. ie when price ...
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2answers
228 views

Can strike prices of options be negative?

I am trying to understand the stochastic model of a financial market in one period by [Föllmer, Schied]. They introduce call and put options for the primary assets, which are non-negative. They do not ...
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0answers
34 views

Where could I get European non-dividend option data

I am pretty new to option pricing. I got a task asking me to price a stock option, which should be an European non-dividend option, and compare my price to its quote. I used to use TSLA data ...
3
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1answer
140 views

Mark Joshi uses forward price to price an option that pays $S_t^2-K$ if $S_t^2>K $ and zero otherwise? Why can we do that?

The following question is taken from Mark Joshi's Concepts and Practice of Mathematical Finance, second edition, Exercise $6.6$ Suppose a stock follows geometric Brownian motion in a Black-Scholes ...
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1answer
137 views

In Carr-Madans option pricing method, why do they use FFT?

In the famous fourier option pricing method by Carr-Madan, (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.348.4044&rep=rep1&type=pdf), the crucial formula is They evaluate this by ...
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1answer
60 views

Show that $Ae^{rt}$ is a solution of the Black-Scholes equation. Why should this be so?

The following is taken from Mark Joshi's Concepts and Practice of Mathematical Finance, second edition, exercise $5.6$. Question: Show that $Ae^{rt}$ is a solution of the Black-Scholes equation. ...
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0answers
29 views

How important is it that numerical methods can price for various strikes simultaneously?

I am reading a paper which presents a numerical method to price call options. Call this Method 1. The method can also price several call-options for a range of strikes simultaneously if you want it to,...
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0answers
49 views

Option PnL Attribution

I am trying to compute the pnl of an option where for the both days option greeks delta, gamma, vega, theta and stock price and IV is given. I know the option pnl will be the sum of delta pnl+ gamma ...
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1answer
38 views

What is the difference between exercise and expiry date?

I know in American options you can exercise the options at any time before expiry date but in European options you can only exercise the options on expiry day. On National Stock Exchange of India the ...
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1answer
37 views

Confusion about bid- ask- and last-prices from option prices data

I’m struggling with the interpretation of quoted option prices I obtained from Bloomberg. The call options prices are available for a daily time series with different strikes at a given day. I ...
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0answers
31 views

Relationship between Calendar Spread Arbitrage and Probability Density Function (pdf)

We all know that the butterfly spread no-arbitrage condition can be expressed as an inequality restriction on the second-order derivative $\partial ^2C/\partial K^2 \geq 0$, which also means the ...
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1answer
17 views

Option symbology with reuters DSWS

I am trying to systematically extract option data at a certain date based on the underlying. Input: interchangeably ISIN/RIC/Mnemonic Output: list of underlying symbols, preferably mnemonics. I am ...
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0answers
10 views

NasDaq/Nyse Option Chain Pre-requisites

Which all Companies are allowed to be traded in the options market? Are there any conditions to allow/disallow a company from trading in the options market? Do we have a list of companies, which are ...
2
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1answer
54 views

Arbitrage opportunity between two call options with strike price \$40, \$30 and cost \$4, \$3 respectively?

Question: Given two call options $c_1$ and $c_2$ with strike price $30$ and $40$ respectively. If $c_1$ costs \$3 and $c_2$ costs \$4, is there an arbitrage opportunity? My attempt: Short $c_2$ and ...
0
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1answer
41 views

Graph of European call option value versus future price

Given a standard European call option on a non-dividend-paying stock. Draw the graph of call price at time $t$ versus the future price $F(t,T)$. The future price $F(t,T)$ is observed at time $t$, ...
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1answer
66 views

Delta of an option which is approaching expiration when stock price decreases

The following is an interview question. It is 10 months since you sold a one-year European call option to a customer. You have been delta-hedging your exposure to the written call since it was sold....
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2answers
78 views

Why are put and call options worth the same despite that put has no upside whereas call has unlimited upsides?

The following is an interview question. All Black-Scholes assumptions hold. Assume no dividends. Consider a standard European call and a standard European put on the same stock. Assume that each ...
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1answer
95 views

Hull-White calibration volatility as a function of time

I need some help for the parametrization of the volatility parameter in the Hull-White model. I have the necessary Caplet vols and I calibrated the HW model to match the Caplet and hence the Cap ...
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1answer
71 views

Hedging delta when gamma is positive

If I have an aggregate position with a positive gamma, should I still be delta neutral? I feel like I'm giving up the positive benefits of being gamma positive because I'm killing my delta constantly.
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1answer
51 views

Calibrating Heston model parameters using the Active-set method and Levenberg–Marquardt

Background: We're estimating the parameters of the Heston model from current market data of options. This is to be implemented using the active-set method (see section 16.5 here) and the Levenberg-...
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1answer
61 views

How does longer time to maturity affect standard European call and put option values?

Denote American call and put option values as $C$ and $P$ respectively. Similarly, denote European call and put options values as $c$ and $p$. It is well known that time to maturity affects all $C,P,...
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2answers
74 views

Future Volatility Trading

I want to find a way to long volatility of a future time period such as longing (march,april) vol from today. My idea is to short a straddle for march and long one for April for example. Will that ...
4
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1answer
186 views

What does is mean by buy(long) volatility or sell(short) volatility in option trading specifically?

I often hear this term quite lot from traders, what does it really mean? And some additional question: In option trading, is "buying vol" equivalent to "buying option" (no matter it's call, put or ...
0
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1answer
106 views

Pricing European call with Feynman-Kac

I am trying to calculate the solution to the Black-Scholes (BS) equation using the Feynman-Kac (FK) formula for a simple European call. According to FK, the solution to BS is the discounted average of ...
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3answers
71 views

Calculate uncertainty of option expiring ITM

I know it is pretty straightforward to determine the probability that an option will expire OTM -- basically a 0.10 delta call will have a 10% probability of being ITM at expiration (see this question)...
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0answers
55 views

Testing Option Strategy

I have a long only momentum system that has back tested well and live results have been ok. I would like to see if I can use these signals to sell Puts to see if it improves results. Not looking for ...
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0answers
47 views

Leverage of various option types

Does the standard European option calculation of leverage, Embedded Leverage = Delta times (Underlying price/Option price) change across the various option ...
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1answer
127 views

Specific Hedge Fund Filed Returns

https://mebfaber.com/2008/12/27/tracking-jim-simons-renaissance-technologies/ But, like always, I will let the data speak for itself. Top 10 holdings, back to 2000, equal weighted through 12/19/2008:...
2
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1answer
113 views

Effective gamma/vega hedging

I want an options position where I can short some options to pocket the premiums and benefit from the time decay. I also want to be vega and gamma neutral. Is there an established way to find which ...
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0answers
44 views

How to hedge payments in a foreign currency?

I´m confronted with solving the following exercise: "Suppose that now is 1 March. You are a UK based exporter who´ll export products to a U.S. company for 250,000 US dollars and to a French company ...
2
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1answer
100 views

How many options would be required to dynamically replicate the VIX nowadays?

The VIX is a portfolio of OTM options on the SPX with non-zero quotes. From CBOE white-paper: Only SPX options quoted with non-zero bid prices are used in the VIX Index calculation. [...] As ...
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1answer
64 views

Cox-Ingersoll-Ross Zero Bond Put Option

according to Brigo & Mercurio (2006): But how is the Zero bond Put of the CIR model? I couldn't find any information about that. Thanks in advance. Regards Chris
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2answers
183 views

Deriving implied volatility programmatically

I'm working on a project to calculate the value of options using Python. I'm using the Black-Scholes model, and I can get accurate results by plugging in a given ...
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0answers
27 views

0 Delta on Forward starting Equity basket option

I wanted to confirm the inherent reasoning behind 0 delta on a weighted equity basket option. For instance, if we have a basket option with a forward starting initial fixing date, we can expect the ...
5
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2answers
502 views

Numeric example to understand the effect of option gamma

Gamma of an option is the second partial derivative of the theoretical value of an option wrt the underlying. It should be the rate of change of Delta wrt to a small change on the underlying. However ...
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1answer
60 views

Variance of a spread for options on spreads

I was reading the paper: https://people.umass.edu/nkapadia/docs/Negative_Vega.pdf In the equation $(5)$, he is defining the variance of the spread as: $$\sigma_1^2S_1^2 + \sigma_2^2S_2^2 - 2\...