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.
1,449
questions
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1answer
13 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 ...
0
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0answers
8 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 ...
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vote
2answers
136 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 ...
0
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1answer
178 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
votes
1answer
178 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
votes
1answer
43 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 ...
1
vote
1answer
76 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
176 views
+50
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 ...
0
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1answer
40 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
51 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
28 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
votes
1answer
80 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 ...
6
votes
1answer
77 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 ...
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2answers
72 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 ...
2
votes
2answers
1k views
Value of Call Option as Volatility goes to Infinity
Why would the value of a call option go infinity as volatility goes to infinity?
I understand how you could solve this question by taking $\sigma \rightarrow \infty$ in the solution to the black ...
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vote
1answer
56 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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1answer
39 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-...
1
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1answer
66 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.
6
votes
1answer
534 views
what's the relationship between forecasted stock volatility and implied volatility?(option)
what's the relationship between forecasted stock volatility and implied volatility? I know that implied volatility is the volatility calculated by BS formula, is there any relationship between implied ...
4
votes
2answers
103 views
What are popular metrics for Option Skew?
What are popular metrics to track skew? Would it be the difference between OTM option and ATM option IV? Would it be a percentage difference in IV?
Also, if both are valid, would a % change be ...
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vote
2answers
70 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 ...
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vote
3answers
67 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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1answer
89 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 ...
4
votes
2answers
230 views
How do I calculate the probability of a short option position expiring worthless?
I want to be able to determine the probability of a short option position (call or put) expiring worthless.
Don't know where to start but I see probabilities derived from the greeks on some web sites?...
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3answers
484 views
How does Rho behaves with moneyness of option?
I was trying to find the relationship between nature of Rho and moneyness of the option.
After finding certain values I found that Rho Value keep increases as the option gets further in the money. ...
2
votes
1answer
114 views
Where can I get some Inflation Option example quotes (year-on-year and zero-coupon)
I am writing an academic paper on calibration of inflation vanilla options.
I need to generate examples for the paper. Is there anywhere I can get example data for the Inflation year-on-year options, ...
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0answers
54 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
41 views
Modelling Theoretical Value [closed]
Quick bit of background. I'm adding a little options market making into my normal crypto derivatives trading, and I'm currently writing the software to help me do that effectively.
One thing I'm ...
2
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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 ...
-2
votes
1answer
121 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
votes
1answer
98 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 ...
4
votes
2answers
167 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 ...
2
votes
1answer
94 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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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 ...
0
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1answer
61 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
0
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0answers
23 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 ...
1
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1answer
57 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\...
5
votes
2answers
492 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 ...
2
votes
0answers
126 views
Bimodal option pricing based on P.D.F
is there any literature on option pricing given the pdf of the underlying asset - e.g. i am interested in seeing how prices for a range of strikes ought to compare based on, say, a simple normal ...
1
vote
1answer
128 views
Simulating assets of different currencies
I have a situation as follows:
One year call option on a Euro stock with a Euro denominated strike.
Knock in feature as follows -
The option can only pay out if the growth in the Euro stock over ...
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0answers
39 views
Hedging option delta
Let's say I am long 1000 50 delta call options. I need to hedge my deltas now. There can be infinite ways to do this. How should I think about proceeding wit this? My first thought was, if the ...
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0answers
62 views
Proving an Expectation
Assume the risk-free bond $B_t$ and the stock $S_t$ follow the dynamics of the Black & Scholes model without dividends. Consider the perpetual American put option with payoff $(K-S_\tau)^+$ when ...
2
votes
1answer
47 views
theta for SPX options vs. E-mini future options
Interactive Brokers currently shows the following data for SPX options at strike 3000 and expiry 2020-09-17:
calls: bid/ask 234.10/236.30, theta -0.362
puts: bid/ask 146.70/148.40, theta -0.225
Then ...
4
votes
1answer
452 views
Numerical simulation of Heston model
I am trying to simulate on Python random paths for a general asset price as described by the Heston model:
\begin{equation}
\begin{aligned}
dS_t &= \mu S_t dt + \sqrt{\nu_t} S_t dW^S_t \\
d\nu_t &...
2
votes
1answer
147 views
Floating Strike Lookback Call Option
Assume the risk-free bond $B_t$ and the stock $S_t$ follow the dynamics of the Black & Scholes model
without dividends (with interest rate $r$, stock drift $\mu$ and volatility $\sigma$).
If $r=\...
0
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0answers
149 views
cashflow for floorlet option on 1 month Libor under Vasicek
I have to figure out the cashflow for a floorlet option written on 1 month Libor under Vasicek model by considering yield curve power series expression and bond pricing equation:
Has anyone an idea ...
4
votes
2answers
520 views
Finding price of the power option
Let's assume a market with $d=1$ and $X=X^1$ satisfying
$dX_t=\sigma X_t\,dW_t,\: \: X_0=1,$
where $(W_t)$ is a standard Brownian motion. Assume that $\mathbb{F}$ is the natural filtration of $X$ ...
5
votes
0answers
466 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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0answers
26 views
Option Bounds in a risk-averse incomplete market
I was reading the article "On option pricing bounds" by Ritchken(1985).
It uses linear programming to determine options upper and lower bounds.
Given a single period model, the stock price will have ...
1
vote
2answers
90 views
Instantaneous change in value of portfolio
I am trying to figure out an intuitive explanation for the instantaneous change for the value of a portfolio (essentially I'm creating a self-financing portfolio to replicate a derivative payoff).
...
