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.
1,696
questions
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1answer
41 views
How does clearing and settlement work in Europe?
I understand the basic trade lifecycle but I can't find more information on how clearing and settlement works. To my knowledge, if I buy VOD LN executed on LSE - this will be cleared by LCH which is ...
2
votes
1answer
49 views
Intuitive explanation of put option pricing based on put-call parity
Assuming no dividends, the put-call parity equation says:
$c + \mathrm{Ke}^\mathrm{-rT} = p + S$
where $c$ is the price of the European call, $p$ is the price of the European put, $S$ is the current ...
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0answers
50 views
Option that never expires
I have been struggling with the problem below for quite some time now. I really don't know how to approach it. All I could think of is to use the Black-Scholes formula with $T \rightarrow \infty$, ...
0
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2answers
91 views
Do basket options have a closed form valuation formula?
Suppose I'm simulating a European call option on a basket consisting of N stocks with slightly varying volatilities but all other parameters remain the same. From the perspective of an estimate, it ...
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1answer
58 views
Why is the liquidity of ATM stock options often relatively low even if the underlying security is being traded in large quantities
I am currently trying to learn more about options trading and option strategies. One thing I have noticed recently is that for a lof of stocks I look up on yahoo finance often a very low open interest ...
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0answers
46 views
Early exercise premium with discrete cash dividends using integral approximation
From my understanding, we have to integrate $N(d1(S_x-D,B,t))$ on both asset-price and time-space to derive the Early Exercise Premium $EEP(B,t)$ on each $t$ before the ex-date to get current early ...
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1answer
224 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
76 views
Swaption PnL approximation/attribution
With a payer swaptions delta and gamma is there a method for approximating pnl for a given move in underlying swap rate? (An equivalent to the Taylor expansion for a vanilla call)
Thanks!
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1answer
93 views
What is volatility trading? [closed]
What is meant by volatility trading? Is it trading 'options'? Aren't options meant to leverage stock prices, and not their volatility?
4
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1answer
77 views
Ratio of the same process at different times
Suppose I have an adapted process $X_t$. I have available option prices on $X_t$ for a range of strikes and maturites. In particular, I have
$$ C_0(K, T_1) = D(T_1)\mathbb{E}_Q[(X_{T_1} - K)_+], $$
...
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1answer
49 views
Options conversion/reversion arbitrage [closed]
I'm trading bitcoin option and i'm trying to find arbitrage opportunity with a synthetic short/long and a long/short future position.
The options are europeans style and settled in BTC. The contracts ...
2
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2answers
322 views
Why does implied volatility decrease without a change in stock price?
I was lookin at some stocks and find that implied volatility changes without the stock price moving too much. What are the causes?
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1answer
42 views
Option trading strategy to test crash risk premium
I would like test if there are "crash risk premia" priced into out-of-the-money puts. My initial thought was to create a portfolio with a short positions in (deep) OTM put options and a long ...
0
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1answer
57 views
Option price quantlib
I am lookin at https://github.com/lballabio/QuantLib/blob/master/Examples/EquityOption/EquityOption.cpp . I want plot a graph of the option price for different underlying prices. Other than changing ...
0
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1answer
129 views
What kind of option would best be suited for a price based algorithm?
So say I wanted to make money off of a simple RSI-MACD algorithm on SPY (ofc this may not necessarily make money, but let's say it does). I'd like to leverage my returns using call and put options, ...
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0answers
47 views
Hedge robustness of the one factor Hull White model
I recently came across a quote in a book:
"All single factor models share the limitation that shifts in curve levels cause shifts in the package of vanilla options that are a good hedge for the ...
1
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1answer
105 views
What is the probability of a lookback option ending in the money (CRR-model)
I would like to compute the probability that a certain lookback option ends in the money, let's say that the option has the following payoff $h_N=\max\left\{0,K-\min\{S_1,...,S_N\}\right\} $ where $K$ ...
0
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1answer
38 views
Asian option sensitivity
I am looking for some materials for profiling all options sensitivities for Asian options with both geometric averaging and arithmetic averaging . The underlying price $S_t$ follows a standard GBM.
Is ...
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1answer
53 views
Market Maker option's pricing with reference spot
When a option's market maker receives a quote from a broker, usually the underlying spot prices is locked with a reference.
Let's suppose the following example:
Broker: "Buy 10k call 2800 of ABC ...
2
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0answers
37 views
What put options would the Universa Tail Fund have bought?
According to this Bloomberg article, Universa was up 3,600% in March 2020, by hedging with extremely out-of-the-money puts: https://www.bloomberg.com/news/articles/2020-04-08/taleb-advised-universa-...
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1answer
72 views
Why my delta position is increasing with increase in spot?
I am trying to take position in future as per the delta position of short put. My strike is 13794 for short put option, spot 10305.3 and volatility is 20.153 then I am getting 5890 position to buy and ...
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0answers
63 views
How Are Option Model Assumptions Justified In Practice
I am reading this article, and I am wondering how comments like
there may be a 50/50 chance that the underlying asset price can
increase or decrease by 30 percent in one period.
are reconciled with ...
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1answer
48 views
Inflation Indexed Caplet/Floorlet
Can someone explain what is it with $\psi_{i}$ (year fraction in $[T_{i-1},T_{i}]$). The formula in Mercurio (2006) as is follows:
$N\psi_{i}P_{n}(t,T_{i})\mathbb{E}_{n}^{T_{i}}\left[\left(\omega\...
0
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1answer
34 views
Predict option IV volatility when I have stock price and previous and next day price
If I have data for IV for the previous day the next da and the stock price in intraday format , can i calculate the option price in intrday format?
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1answer
54 views
Can you simulate an option position at a strike when that does not exist
Is there any way to simulate buy an option at a pric of x when that price is not available to buy ? If x-3 and x+3 exists, how do I buy it at price x?
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1answer
167 views
Power Options & Forwards on Stock Squared
Short story: the process for Stock price squared is not a martingale when discounted by the money-market numeraire under the risk-neutral measure. How can we then compute derivative prices on $S_t^2$ ...
3
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1answer
100 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
4
votes
1answer
113 views
Can “Turbo warrants” be priced using the Black & Scholes model?
I am trying to model the pricing of an asset called a "Turbo warrant", which to me looks a lot like a Down-and-Out Barrier option with leverage. When the price of the underlying asset hits a ...
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0answers
28 views
How to calculate Greeks for leveraged Barrier options?
I am wondering how to calculate option Greeks for Down-and-out barrier Call options with leverage.
The option characteristics are as follows. The buyer of the option pays a fraction of the spot price <...
3
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0answers
2k views
Black-76 Model for Swaption Price and Greeks
I'm in the early stages of developing a swaption pricing model.
Suppose $t_1$ is the tenor of the swap rate in years, $F$ is the forward rate of the underlying swap, $X$ is the strke rate of the ...
3
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0answers
90 views
How is the implied risk neutral density affected when changing numeraire?
For example i would like to price
\begin{equation*}
E^{Q} \left[ e^{-\int_{0}^{T}r_{s}^{cur}ds} f \left( S_{T_f}^{cur_1} \right) | \mathcal{F}_{0} \right] = B_{cur}(0,T)E^{Q^{cur}_{T}}[ f(S_{T_f}^{...
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2answers
76 views
Why are these deep in-the-money FLEX options seemingly bought at a discount?
98% of the initial reference value is .98 x 267.88 dollars, which equals 262.52 dollars. However, the market value of each call contract they purchase is 247.42 dollars.
How are they purchasing these ...
2
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2answers
329 views
Confusion about replicating a call option
Assume standard Black-Scholes model,
$$dS(t)=S(t)(rdt+\sigma dW(t))$$
where $\sigma$ is a constant and $W(t)$ is a Brownian motion under the risk neutral measure.
A call option is replicable, so if we ...
1
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1answer
63 views
Deriving Forward Vol from Straddle and Put Spread
Assuming we have the fair value of the July straddle on a certain strike, what would be the implied July-Oct forward vol if an order comes in to sell the July-Oct Put Spread (on the same strike) for a ...
8
votes
2answers
398 views
What is the industry standard pricing model for CME-traded Eurodollar future (American) options?
The CME-traded Eurodollar futures option is an American option.
What is the industry standard pricing model for this product?
Does the industry practice to treat CME-traded Eurodollar futures ...
2
votes
1answer
202 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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1answer
90 views
VIX vs S&P: Drift in the hedging residual?
I am looking at the daily returns of the VIX index (dVIX ) and the daily returns of the S&P 500 (dS).
I am running a linear regression (using 0 intercept) and get a regression slope of -1.4, i.e.
...
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0answers
49 views
How do I achieve a Long Gamma, Short Theta Exposure?
How I understand it is that if I:
Sell OTM near dated put which will pay high theta and have low gamma
Buy ATM long dated put which will have low theta and have higher gamma
However, if there is a ...
8
votes
2answers
9k views
Gamma Pnl vs Vega Pnl
Why does Gamma Pnl have exposure to realised volatility, but Vega Pnl only has exposure to implied volatility? I am confused as to why gamma pnl is affected (more) by IV and why vega pnl isnt affected ...
2
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1answer
384 views
Implied Vol skew VS Local Vol skew (as presented by Derman 1995)
I am reading Derman's article/notes regarding local volatilty:
http://www.emanuelderman.com/writing/entry/the-local-volatility-surface.
I am examining the graph on page 13.
The Implied volatility (...
2
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1answer
94 views
What is the name (Greek) for sensitivity of an option's Theta to the Time to maturity?
All other second order sensitivities of option prices to underlying price, volatility and time, seem to have a commonly accepted names: Gamma, Vanna, Charm, Vomma/Volga, Veta as documented here (...
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0answers
46 views
Do barrier options have closed form values for Greeks?
This may be quite simple but I was wondering if barrier options, and more particularly up-and-out European call options have closed form values for the Greeks?
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0answers
59 views
Summary of Pricing Options of Log-Normal Claims Using Black's Formula
Cross posted from here.
Let $B$ be a $Q$-Brownian motion and $X^{s,x}$ given by
$$dX_t = X_t(\mu_t dt + \sigma_t dB_t),\quad X_s = x$$
for $\mu, \sigma$ deterministic. Let $\mu_{s,t}=\int_s^t \mu_u du$...
2
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1answer
39 views
Far OTM calculation issue on Bjerksund-Stensland
Has anyone come across and fixed calculation issues on boundaries using Bjerksund-Stensland 2002 (Hull, Haug or Rouah implementations) ?
Thanks in advance
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1answer
174 views
Why risk-free interest is needed for Margrabe's Formula?
The source code for Margarble's formula in QuantLib is here. The implementation requires a forward price be computed:
...
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3answers
329 views
Who trades exchange options in practice (Margrabe's formula)?
I'm currently studying the pricing of the exchange option.
https://en.wikipedia.org/wiki/Margrabe%27s_formula
While I can appreciate the theory, who actually buys these options in practice? Are ...
6
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1answer
82 views
Should I hedge this spread with a spread option or an insurance product?
My firm generates electricity from wind. Accordingly, most of my generation takes place at night, when prices are low -- and, due to congestion / oversupply, often sharply negative -- so much so that ...
5
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2answers
215 views
Higher moments of a straddle
Following the logic of Ben-Meir and Schiff (2012) and this question the first, second, third and fourth raw moments of a put are:
Similarity, for a call it is as follows:
where
and
...
0
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1answer
78 views
Why do replicating strategies delta hedge?
We have a simple BS-market of one risky asset $S_{t}$, a bond $B_{t}$ and a digital option $X$ on the risky asset with value process $V(t,S_{t})$. I was able to derive $V(t,S_{t})$ using risk-neutral ...
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4answers
1k views
Implied Vol Smile: from Calls, Puts or Both?
This might be a simple question, but I couldn't find the answer anywhere: is there a separate Volatility smile (and surface) based on Calls and a separate Volatility smile (surface) based on Puts? Or ...
