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.
1,342
questions
2
votes
0answers
34 views
Why do coefficients flip after the including a lag in the optimisation? implied volatility/skewness/ivspreads
I'm hoping some of you guys can help me out. I am applying the paramametric portfolio optimisation of Brandt, Michael W., Pedro Santa-Clara, and Rossen Valkanov. in which the weights on specific ...
0
votes
0answers
20 views
Hedging an option on a non-traded asset in BS world
I have given the following task given.
Suppose you are in a Black-Scholes World where you have the standard assets
$$ dS_t = \mu S_t dt + \sigma S_t dW_t $$
$$ dB_t = r B_t dt $$
and now you also ...
0
votes
0answers
9 views
Black-Derman-Toy model AND European-type bond call option
In a Black-Derman-Toy model in which Ω ={ ω1, ω2, ω3, ω4 }, the risk-neutral probability for each state ωi, i = 1, 2, 3, 4 is 1/4 . The spot rates in BDT model are given as follows.
ω r1 r2 ...
35
votes
5answers
67k views
A simple formula for calculating implied volatility?
We all know if you back out of the Black Scholes option pricing model you can derive what the option is "implying" about the underlyings future expected volatility.
Is there a simple, closed form, ...
2
votes
1answer
21 views
How to price a phoenix and snowball type autocallable options?
I'm currently studying the pricing of autocallable options, especially snowball (accumalated coupon) and phoenix (accumlated coupon, but the coupon may also be autocalled if the underlying price ...
18
votes
4answers
16k 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 ...
3
votes
0answers
24 views
Does convexity in the IV space means convexity in the price space?
Let's assume that we only look at OTM options to construct a Risk Neutral Density (RND).
As the RND is the second derivative of the price of the option with respect to the strike, we would expect ...
1
vote
1answer
61 views
OTC Derivatives Moneyness Conventions
When looking at the OTC Derivatives market, is there a standard moneyness convention that is applied? And if so, what is that bucketed approach? For example: 90%-110% for ATM, 70%-90%, 110%-130%, etc.....
1
vote
1answer
252 views
Basic Replication of European Call Option
I am looking at the very basics of replicating an option with a portfolio of risky and risk free assets. As such we can define a portfolio of $x$ no. of shares, $y$ bonds & $z$ options at time $(T)...
2
votes
1answer
33 views
Settlement of currency options
wanted to understand the market action done to settle a call option.
Let's say I entered into a export seagull for eurusd and on the date of expiry my sell call gets exercised. Assuming that my sell ...
2
votes
1answer
98 views
How does the volatility skew/smile relate to hedging/trading vanilla contracts?
I know that obtaining and calibrating the smile is important in the hedging and trading of exotics since we use vanillas to hedge and price exotics. How is the smile important in the hedging and ...
5
votes
2answers
5k views
How to derive Black's formula for the valuation of an option on a future?
I've got a question about 1976 Black Model and Bachelier model.
I know that a geometric brownian motion in the P measure $dS_{t}=\mu S_{t}dt+\sigma S_{t} dW_{t}^{P}$ for a stock price $S_{t}$ leads (...
25
votes
4answers
1k views
Who has introduced the term 'vega' and why?
The sensitivity of the option value $V$ to volatility $\sigma$ (a.k.a. vega) is different from the other greeks. It is a derivative with respect to a parameter and not a variable. To quote from Paul ...
4
votes
1answer
122 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 ...
0
votes
0answers
28 views
Negative drift when calibrating GBM parameters
Setup for question:
Consider a basket of $N$ stocks $\{S^1, S^2, \dots, S^N\}$. For fixed strike $K$, each stock in the basket, $S^i$, follows the SDE
$$dS_t^i = \mu^i(t) S_t^i dt + \sigma^i(K, t) ...
2
votes
2answers
108 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 ...
2
votes
1answer
152 views
Why is put-call parity defined differently by CME and Wikipedia?
In general, Wikipedia defines Put-Call parity as:
C - P = D(F - K)
----------------
C = call price
P = put price
F = *FORWARD* price
K = strike
which can be re-...
1
vote
0answers
59 views
option model value vs market price
In my job as FX trader we use as option pricer a variant of B&S.
We use that model for “accounting” purpose, i.e. for storing the daily P&L of the portfolio, and also for control the trading ...
1
vote
1answer
115 views
Implied volatility equality for deep in/out-of-the-money put and call
Someone posed the following question.
Given a strike $K$ and the stock price $S$ and the same maturity are the implied volatilities of the call and put with these same parameters equal for $|S-K|\gg0$...
2
votes
3answers
401 views
How to synchronize put and call option-data?
I recently retrieved a large amount of European option data, for call and put prices, from OptionMetrics. Doing so for the same time period I get a file consisting of
62558 rows of call prices & ...
0
votes
1answer
42 views
How do I calculate option payoff before its expiration date? [closed]
How do I calculate option payoff before its expiration date? For example, if I long a 6 month call with K = 11100, T = 0.5, p = 150, what would be the payoff of the option if I exercise it in 3 months ...
2
votes
1answer
167 views
Can someone explain rigorously Taleb's criticism of Nate Silver's election forecasting?
Taleb makes the claim in this paper (and others) that there exists some sort of bound on the variance of a binary forecast such that if a forecaster's binary predictions exceed the bounds on variance ...
7
votes
3answers
688 views
Creating Options Database
I am trying to create a database which will hold information for various stock options and will need to be updated daily. The idea is to use this database to keep track of changes in the open interest ...
0
votes
1answer
153 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 ...
0
votes
1answer
31 views
Can someone provide a good definitive explanation for rho in relation to option risks?
I have a pretty good understanding of option risks except for one thing, rho. Unfortunately, interest rates tend to have a small effect on option prices, and thus most literature tend to just gloss ...
0
votes
1answer
44 views
Why is the value of the Brownian motion bounded by the maximum value of this square difference?
This comes from Taleb and Madeka's paper (https://www.academia.edu/39998351/All_Roads_Lead_to_Quantitative_Finance_Response_to_Clayton_?auto=download) regarding arbitrage restrictions on binary ...
3
votes
2answers
514 views
how to define liquidity in equity, index, and etf options
i've heard several ways to put a metric on liquidity of options.. obviously liquidity isn't a constant.. things like the Bid/Asks spread, liquidity of the underlying.. Trying to find a way to ...
17
votes
3answers
443 views
How do you characterize dividends for equity options?
While many systems like to treat dividends as a continuous yield when pricing equity options, it works quite poorly for short-dated options.
In the short run, deterministic dividends are clearly the ...
0
votes
0answers
19 views
Volatility Skew fitting in R; Calculate option delta using various volatility dynamics
Given a fixed maturity option chain, i was wondering if there is any way to evaluation an option against this volatility surface and compute the various delta of the options wrt to volatility dynamics ...
0
votes
1answer
51 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 ...
1
vote
2answers
94 views
Option quotes or trades: Which one is more informative?
Suppose I have quote data as well as real transaction of option contracts? I was wondering if the informational content is the same. On the first hand, quotes show the intention of seller/buyers on ...
10
votes
3answers
5k views
How to exploit calendar arbitrage?
Say we are looking at European Call options in a toy environment with zero deterministic interest rates, a stock paying no dividends, no repo rates etc...
Let $C(T,K)$ be the price of a call with ...
3
votes
2answers
118 views
Pricing a government bond
I am reading the "Bond" article on investopedia on stumble on the way they price a government bond.
Say that the interest rate at time $t=0$ is $r=10\%$. I buy a government bond with face value 1000\$...
3
votes
2answers
123 views
Does high levels of vol-of-vol parameter in SABR lead to Arbitrage? (Something seems wrong with Hagans formula)
Main question: Do we need to restrict the vol-of-vol parameter in SABR further than $\text{vol-of-vol}>0$ and how do we determine the interval of vol-vol which the model is arbitragefree?
...
2
votes
0answers
56 views
How to determine expected returns of an options portfolio?
Lets say I have a delta neutral portfolio, iron condors on spy for example. I'm short a call credit spread and a put credit credit spread of equal widths. I would like to determine the expected ...
2
votes
1answer
120 views
How to quantify the Variance Risk Premium (VRP) with probability density functions?
The VRP is usually displayed by charts like this one:
It's easy to see that, for most of the time, options are priced by using volatility which will reveal itself larger than the realized one. So VRP ...
2
votes
0answers
34 views
Rainbow option pricing formula under *Bachelier* model
Let's consider a call on min option on two underlying arithmetic Browniation motions $V_t$ and $H_t$ (no drift). Let $P_t$ denotes the price process of the option, $r$ the riskfree rate, $\tau$ the ...
0
votes
0answers
17 views
EMTN with two barrier options and pricing by Monte Carlo method
I analyzing an EMTN (Euro Medium Term Note) for my Master's degree thesis, which uses 2 barrier options:
a Down and In put,
an Up and In put
However, I only know how to do it for Knock-out options. ...
1
vote
0answers
30 views
B-S derivative with another boundary condition
I want to use the derivation of BS for another type of derivative, not an option. Known the derivation of the Black-Scholes differential equation, is it possible to use in the same equation when my ...
1
vote
0answers
26 views
Price moneyness vs spread moneyness for credit index options (CDX HY)
Is spread moneyness equivalent to price moneyness for volatility surfaces of CDX HY? In other words, is the ISDA converter a linear transformation?
I have market data that I need to convert to input ...
0
votes
1answer
66 views
Option and probability of finishing in the money?
This seems to be another easy question but I am a bit confused. I know delta is a proxy for an option finishing ITM. Delta also happens to be N(d1) in the BSM pricing model. N(d1) usually is pretty ...
2
votes
1answer
91 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, ...
0
votes
1answer
48 views
Can someone explain to me the intuition behind the discount factor for this simple payoff? [closed]
Let's say you enter into a contract today in which in time t, you receive the difference between the underlying stock price and 100. Denote the stock price as S. Why is today's value of such a ...
0
votes
1answer
68 views
How do we calculate option payoff before expiration?
I am trying to simulate a bull spread option
and I have used an online tutorial to calculate payoff at expiry but I am having difficulty simulating the payoff ...
1
vote
1answer
53 views
Modifying Basic Black Scholes Equation For Time Dependent Variables - Per Wilmott?
I am reading Wilmott's book and don't understand why he makes the following step to re-write the PDE. I get equation 8.4, that's just the typical PDE for a dividend yielding stock where r(t), D(t) ...
0
votes
1answer
44 views
Intrinsic value vs Time value of an option: what's the purpose/motivation for their definitions? [closed]
I am an actuarial student and our text has the following definitions:
Intrinsic value: This is the payoff assuming the expiry of the
contract immediately rather than at some future time.
...
1
vote
1answer
68 views
SABR Implied Vol: Normal Approximation vs Log-Normal Approximation
I am having trouble understanding the difference between the normal and log-normal implied volatilities from Hagans SABR model: http://web.math.ku.dk/~rolf/SABR.pdf.
As far as i understand the main ...
1
vote
1answer
43 views
Hindsight overhedge for pricing path dependent options
I understand how to use the longstaff schwartz method in Monte Carlo to compute the continuation value of path dependent options but someone recently mentioned another technique called "Hindsight ...
2
votes
1answer
72 views
Do Perpetual American Options have closed form functions to compute the Greeks?
I was wondering if there were analytical formulas to compute delta or gamma for perpetual American options?
4
votes
1answer
2k views
What equation will convert implied yield volatility to implied price volatility?
I am trying to figure out how to turn implied yield volatility of a short-term interest rate into implied price volatility. Is there an equation to do this?
I have come across the equation for a ...
