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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0
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2answers
111 views

Which interest rates to use for options pricing?

I am looking at the historical treasury interest rates and am uncertain which rates would be best to use for options pricing. Should I use 1 month, 6 month, 2 year? See: ...
1
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2answers
31 views

Why is the vega of an at the money option so insensitive to movements in volatility? I.e, why do ATM options have such little Vomma?

I've been trying to understand why at the money options have very little vomma. I was reading and came across a graph that showed vega as volatility changes and I couldn't grasp how the relationships ...
1
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0answers
18 views

Straddle neutral strategy

What does it mean to implement a delta-neutral strategy for straddle ? A straddle consists in buying a call and a put simultaneously, at the same date, on same underlying, with same maturity and ...
6
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4answers
459 views

Replicating portfolio and risk-neutral pricing for interest rate options

For equity options, the pricing of options depends on the existence of a replicating portfolio, so you can price the option as the constituents of that replicating portfolio. However, I am not seeing ...
7
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2answers
3k views

What causes the call and put volatility surface to differ?

I currently have a local volatility model that uses the standard Black Scholes assumptions. When calculating the volatility surface, what causes the difference between the call volatility surface, ...
3
votes
1answer
61 views

Which volatility to use to price options on futures contract?

I have some questions regarding pricing futures options and I just want to be sure that my thoughts are correct. I am trying to price options on futures for american & european style. In the ...
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0answers
40 views

Volatility Surface Constituents, do's and dont's

Recently I have been working a lot with implied volatility and volatility surfaces. The basic idea is easy to follow: 1) Gather market prices of options at different (Strike,Expiry) 2) Calculate ...
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0answers
9 views

European vs American forex options availability [on hold]

I am interested in buying some puts on a forex major cross. I see that most of the brokers offer just American options... am I wrong? My question is: is it possible to "simulate" the behaviour of an ...
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1answer
50 views

Why does expected price of OTM option not equal to BS price?

If I assume that stock returns follow normal distribution with drift = 0% and S.D. = 10%. In the long, if I keep investing in this stock for a year with the same capital every year for a consecutive ...
-2
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2answers
33 views

Option greeks: sensitivity to 1% move

In a Black&Scholes framework how can I compute the following sensitivities: to 1% move in the underlying price to 1% move in implied volatility I would like the greeks to tell me how many ...
5
votes
2answers
289 views

Pricing options under restricted domain

How would I price an option when the underlying security is unable to trade above a certain price? I assumed this would be as simple as restricting the limits of integration of the PDF to B (the ...
1
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0answers
29 views

Time-independent local volatility

Suppose somebody provides us with a surface of European call prices $C(\tau,K)$ where $\tau$ stands for time-to-maturity and $K$ for the strike. By Dupire's results, there is a unique local volatility ...
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1answer
62 views

negative probabilities in the bivariate tree heston model

I am trying to implement the bivariate tree approach for the Heston model by Beliavea & Nawalkha. I currently have the problem that given the specifications in their examples, I always obtain ...
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0answers
30 views

How to value an expansion option?

Fair warning this is help with homework. I am not asking for an answer but some guidance or a formula would be nice. I have absolutely no background in finance and this class is online with no ...
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0answers
12 views

How does implied volatility of puts relate to strike price in presence of negative news? [duplicate]

There is a lot of literature available but i don't kind understand that if there is a negative news about a stock with the traders why do puts with lower strike tend to have higher implied volatility ...
2
votes
2answers
135 views

Is it fair to assume $(ud=1)$ in the binomial tree option pricing model?

I have discussion with my colleague on why a general assumption $$ud=1$$ in binomial tree option pricing model would be necessary? I take it a simplification of the problem, otherwise, there will be ...
2
votes
0answers
43 views

Why is this delta-hedging/P&L example on a variance swap call correct?

I'm looking into this article about var swaps: http://sbossu.com/docs/VarSwaps.pdf and not sure how to correctly interpret Exhibit 2.1.1. "In this example an option trader sold a 1-year call ...
2
votes
3answers
330 views

Any New Discoveries in Quantitative Finance?

It seems like the field has become stagnant in the decades following the enormously successful and influential Black Scholes model. (The original paper has been cited a staggering 25,000 times - more ...
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1answer
85 views

is Sum of P&L equal to portfolio value

For a portfolio containing FX options, would the sum of P&L for each option be the portfolio value?
4
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1answer
94 views

What is the mechanism of Asian option?

I have no problem with the mathematical definition of an Asian option. For example, assume the strike price is $K$, the expiration date is $T$, the underlying asset has price $S(t)$, and the payoff is ...
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2answers
121 views

Why is the price of a call option with $K=0$ equal to the price of the stock $S_0$?

In a case of a call option with strike $K=0$, then payoff at expiration time $T$ is equal to: $$(S_T-0,0)^{+}=S_T$$ In reality the price of the option on the date of maturity is never equal to the ...
3
votes
1answer
122 views

Data Selection for Empirical Pricing Kernel Estimation (Stochastic Discount Factor)

I want to estimate an empirical pricing kernel for an index. Hence, I need to estimate a physical and risk neutral density. For estimating the physical density, only the index data in an observed time ...
2
votes
1answer
122 views

Some questions about implied volatilities and how to generate theoretical prices when market prices are not available

I am building a little Excel file that take some option prices in input and plots the volatility smile/surface. I have a script that reads market prices from the option chain for 3 different ...
2
votes
1answer
77 views

Price an option whose strike price is always lower than the future price of the security

Suppose it is known that the price of a certain security after one period will be one of the $m$ values $s_1,\ldots,s_m$. What should be the cost of an option to purchase the security at time $1$ for ...
2
votes
2answers
139 views

How to exploit calendar arbitrage?

Say we are looking at European Call options in a toy environment with zero deterministic intereset rates, a stock paying no dividends, no repo rates etc. Let C(T,K) be the price of a call with expiry ...
0
votes
1answer
92 views

Gamma is always positive on both put and call

I recently met the claim that for standard put and calls the gamma of the options are always positive. Is this a general result? I am hoping not to assume any model, especially not Black-Scholes.
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2answers
81 views

VaR for European Call

I have a European call option with current stock price $S_0$, strike $K$, risk-free rate $r$, volatility $\sigma$, and time to maturity $T$ years. I assume that the stock price at time $t$, which is ...
2
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1answer
71 views

Effect of time to maturity on european put option

Let $C(K,T,S_0)$ denote the price of an European call option with strike K and maturity T on underlying price $S_0$. Assume interest rate $r>0$. Then of course $C(K,T,S_0) \geq 0$ and $C(K,T,S_0) ...
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2answers
69 views

Anybody knows the answer to this exercise found in PWIQF?

I got this question from the last exercise of chapter 2 from "paul wilmott introduces quantitative finance" book. Appreciate your help.
2
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1answer
84 views

Asymptotic behavior of theta of vanilla call option

It is well known that the theta of call option is always negative. Also, the theta of (at the money call option) goes to infinity as the time approaches to the maturity. On the other hands, (ITM and ...
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2answers
111 views

How market making in Index options is done?

I have been thinking about this one for last couple of days. With options on share we hedge on cash and the underlying equity as per Black-Scholes formulation. But I am confused on Index options. ...
2
votes
1answer
54 views

Exercise on American call option and dividends

Consider an americal Call option on an underlying paying dividends. Then it is often argued that it is only optimal to exercise right before the dividend is paid out, otherwise one will not exercise. ...
0
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1answer
44 views

I have some historical options data, and there are duplicates of some options, how to filter them

I have some historical EOD options data for 2013, and there are duplicates listed for same strikes/expirations. I was told that by the provider that this is due to "special one-time cash payout" for ...
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1answer
103 views

Moneyness and option prices

I'm attaching stock prices from CRSP to a dataset of option prices in order to compute the option moneyness. I'm wondering whether I should adjust the underlying prices taking into account splits and ...
1
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1answer
71 views

How to calculate the probability of 2 options ending in money with different expiration dates?

Lets say I make a trade that consists of buying one put and 2 calls of the same underlying but with different expiration dates and different strikes. Example trade: ...
1
vote
1answer
100 views

Historical Implied Volatility Calculation

I'm trying to calculate implied volatility for the FTSE 100 for the last few years. I have all the end of day data from LIFFE for the last few years. I have combined the data by weighting the ...
3
votes
1answer
178 views

How to synthesize a futures spread option?

Is it possible to synthesize a futures spread option using only the options on the spread's underlyings? If so, how? If not, is there another way? As an example, please show me how to synthesize ...
1
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2answers
105 views

Which risk free rate is assumed by market when pricing american options?

I'm just started with finance, so maybe my question is dumb or answered elsewhere. Please guide me to relevant materials. According to put-call parity more time to expiration means more difference ...
4
votes
6answers
7k views

How to calculate stock move probability based on option implied volatility and time to expiration? (Monte Carlo simulation)

I am looking for one line formula ideally in Excel to calculate stock move probability based on option implied volatility and time to expiration? I have already found a few complex samples which took ...
4
votes
5answers
2k views

Call vs. Put Option

I have two interrelated questions that have been bothering me for some time. I have read all the stuff online and it still doesn't make sense to me: Let us assume: 0% interest rate (both hedge ...
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3answers
172 views

forward implied volatility skew

I would like to calculate implied forward volatility skew. I have stochastic volatility monte carlo. What kind of payoff do I need to price and how to use Black() formula to calculate the implied ...
3
votes
0answers
85 views

How do I calculate the probability of a stock being above or below a value using the Heston model?

How can I use the Heston Model to calculate the probability of a stock being above or below a certain value on a given date in the future?
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0answers
47 views

Opposite of hard to borrow?

If market participants are certain a stock will suffer a huge decline, the shares will become hard to borrow and an interest fee will be applied to borrow the stock. This interest fee eliminates the ...
0
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0answers
25 views

How to generate jump times in in Multilevel path simulation for jump-diffusion SDEs?

I am trying to generate jump times in in Multilevel path simulation for jump-diffusion SDEs using the following MATLAB code: I used following Algorithm in Yuan Xia paper: But I have not reached ...
4
votes
1answer
179 views

Analysis of Unbalanced Covered Calls

Hello I am doing an analysis on covered calls with and extra amount of naked calls. Ignore the symbol and current macroeconomic events. I couldn't find any reference to this strategy (unbalanced is ...
6
votes
2answers
145 views

Does it make sense to use upward and downward volatility in option pricing?

Historically stocks have a higher likelihood to increase in price than to fall in price. As such would it make sense to split a stocks volatility measurement into upward and downward components? For ...
4
votes
5answers
906 views

Do binary options make any sense?

Reading from "www.nadex.com" - the copy reads "Binaries are similar to traditional options but with one key difference: their final settlement value will be 0 or 100. This means your maximum risk and ...
1
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1answer
54 views

When $C(K_2) = C(K_1)$ for call options with the same expiration date

The exercise is to show $C(K_1) \geq C(K_2)$ where C(K) denotes the value of a call option on a stock price S with strike price K. We assume the expiry is the same for both. I have proved this by ...
4
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1answer
273 views

What are the main flaws behind Ross Recovery Theorem?

Stephen Ross’ new paper claims that it is possible to separate risk aversions and historical probabilities if the Stochastic Discount Factor is transition independent using Perron-Frobenius Theorem. ...
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0answers
60 views

FX Delta Conventions

I'm currently reading Iain Clark's book Foreign Exchange Option Pricing and I got stuck at one sentence in the beginning of Section 3.3 that I feel is important to understand. He writes: FX ...