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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Risk-neutral price of $H=e^{X_T^1+X_T^3}$
Let $B=(B_t^1,B_t^2,B_t^3)$ is a $\mathbb R^3$-valued Brownian motion.
Let $r_t$ (risk free rate) be bounded and deterministic.
Let consider the DISCOUNTED market $$dX_t=\frac52dt+2dB_t^1-dB_t^2-dB_t^...
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1answer
50 views
Where can I find data about Options for Europe (entire dataset)?
I need to get data about the entire dataset (i.e. all) of options for European countries. Where can I do that?
For example, if I had to do it for US options, I would just use WRDS (to which I have ...
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1answer
77 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 ...
7
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1answer
504 views
Risk management tools for long term Gamma/Vega sellers subject to margin calls
TL;DR: if you're a retail investor and you systematically sell long-term vertical spreads while staying Delta-neutral, your main risk comes from Vega and the Gamma of opening gaps that can throw you ...
3
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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
167 views
VXX Put pricing
Last week at Friday's close, the Dec 14 37.5 Put options were selling for \$.68 with VXX at \$40.29. This week at Friday's close, the Dec 21 37.5 Put options were selling for \$.38 with VXX at \$40.50....
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1answer
18 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 ...
5
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1answer
603 views
Calculating dealer gamma imbalance/exposure for an options strip
Have seen this being done for years (primarily by J.P. Morgan and a couple other bank research desks) and am attempting to re-create for my own personal research. I’ve read the forums on here but no ...
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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
118 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
97 views
In literature, is IV constantly adjusted during option delta hedging?
In a lot of literature, they like to compare the performance of buying an option, and then delta hedging either at that options implied volatility (IV) or the true future volatility. This is under ...
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14answers
19k 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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1answer
65 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\%$ ...
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1answer
52 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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4answers
294 views
How to calculate return on investment for an adjustment to a complex options position?
Say I currently hold a set of options positions with the same symbol/expiry that collectively have a net present value based on the estimated value at expiration of +10. I could also liquidate the ...
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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
70 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
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 ...
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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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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
79 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
44 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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1answer
288 views
Exercise Probabilities Vanilla Cap/Foor
When looking at the discounted pay-off formulas of a vanilla caplet and a vanilla floorlet
$\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_k-r_{cap},0)$
$\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_{floor}-...
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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 ...
2
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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
61 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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1answer
138 views
Which securities have expirations more often than monthly?
I'd like to explore buying low-cost calls close to the money, so I'm looking for low time values in options premiums. This happens near options expiration.
Unfortunately, most options expire on the ...
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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,...
3
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2answers
143 views
American Option Exercise
Suppose I am a market maker in American options. At end of day I have positions in various options but my portfolio is overall hedged. Now, after the market close, someone decides to exercise an ITM ...
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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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51 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
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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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 ...
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2answers
144 views
Proving a process is martingale under the Risk Neutral Measure
Show that for any $\lambda \in \Re$, the process $Y_{\lambda,t}$ defined as:
$$Y_{\lambda,t} = (S_t/S_0)^\lambda e^{-(r\lambda-\lambda(1-\lambda)\sigma^2/2)t}$$
is a martingale under the risk ...
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1answer
181 views
How to show arbitrage when a European option price is greater than the no-arbitrage price?
My example is:
Current price = 20,
If it goes up it'll be worth 22, if it goes down it will be worth 18
risk free rate: 12%, time = 3 months
Strike = 21
call option is worth 0.633
I know that if the ...
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 ...
2
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1answer
55 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 ...
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1answer
79 views
Why Joshi defined option value to be discounted payoff using risk neutral expectation?
Currently I am reading Mark Joshi's The Concepts and Practice of Mathematical Finance.
At page $59,$ the author mentioned the following.
Instead
of requiring that every portfolio should have ...
3
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2answers
198 views
How to adjust delta hedging if stock price decreases?
Question: You are long a call option no MITCO stock. You have delta hedged your position. You hear on the radio that the CEO of MITCO has just been arrested for running a massive Ponzi scheme. The ...
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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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0answers
31 views
Hedging a long position-one period from Steven Shreve Stochastic Calculus for Finance
The following question is taken from Steven Shreve Volume 1, Chapter 1, Exercise $1.6$ (Hedging a long position-one period)
Consider a one period binomial stock model with $S_0=4$, $S_1(H)=8$ and $...
2
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1answer
96 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
78 views
Show that $\frac{\partial c(t))}{\partial \sigma^2 }>0 \text{ if and only if } S(t)<Xe^{-r(r+\frac{1}{2} \sigma^2 )(T-t)}.$
Statement: if $c(t)$ is the price of the digital cash-or-nothing call option, then direct calculation (under Black-Scholes assumptions) shows that
$$\frac{\partial c(t))}{\partial \sigma^2 }>0 ...
