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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2answers
17 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 ...
1
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0answers
18 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 ...
0
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0answers
10 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 ...
0
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0answers
24 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 ...
2
votes
0answers
41 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
305 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 ...
4
votes
1answer
90 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 ...
1
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2answers
120 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 ...
1
vote
1answer
117 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 ...
0
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1answer
89 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.
1
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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
votes
1answer
65 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) ...
0
votes
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 ...
2
votes
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 ...
1
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2answers
109 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. ...
1
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1answer
69 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: ...
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. ...
1
vote
2answers
103 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 ...
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?
0
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1answer
78 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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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 ...
3
votes
1answer
119 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 ...
6
votes
2answers
143 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 ...
1
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1answer
99 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 ...
1
vote
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 ...
0
votes
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?
0
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0answers
55 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 ...
0
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0answers
36 views

Derivation of the formulas for the values of European asset-or-nothing and cash-or-nothing options

The asset-or-nothing European option pays at t = T the value of the stock when at time T that value exceeds or is equal to the exercise price E, and nothing if the value of the stock is below E. So, ...
0
votes
1answer
54 views

Delta formula for FX vanilla option

What value do you use for annual dividend yield? It does not apply in case of FX.
-1
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1answer
49 views

Is the price of a binary call not monotonous with vol for OTM

Is this true and how would you prove it
3
votes
2answers
117 views

Is there a better way to price options than with historical volatility?

I know that annualized historical volatility calculated with closing prices is a much rougher estimate than implied volatility for the correct "volatility" parameter in options pricing models. ...
1
vote
1answer
63 views

Binary option expression

Given r=0, σ(K)=const Binary=lim┬(ε→0)⁡〖((C(K,σ(K))-C(K+ε,σ(K+ε))))/ε〗 What is the analytical expression for the binary option value? σ(K)=const Therefore, Binary=lim┬(ε→0)⁡〖((C(K)-C(K+ε)))/ε〗 ...
2
votes
2answers
114 views

C# - Using Black Scholes Newton returns NaN occasionally

First caveat: I'm a programmer doing this for a client, and my knowledge of options probably has holes in it. So be a little forgiving here. =) The Issue: When I run Black Scholes Newton against ...
1
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2answers
67 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.
0
votes
0answers
44 views

European style average price option Delta

I use a numerical method to calculate the value and Greeks of an European style average price option, e.g., with a given volatility, I simulate 1000 random walk price paths find the average value ...
0
votes
1answer
29 views

Normal vol - convention

apologies for the simplicity of the question, but I was wondering: what is the quoting convention for normal (bps) volatility? Say I have the following time series of data: Date Close Abs Change ...
0
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0answers
18 views

Residual maturity vol

The following question is probably (from a practical point of view) more relevant for EM markets which typically exhibit a more pronounced forward volatility compared to spot volatility. Say I buy a ...
0
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0answers
12 views

Option platforms providing eurex products

I search an option platform providing eurex products as eurostoxx 50. Can you advice me some platforms ? Thank you in advance for your answer Julien
2
votes
2answers
133 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 ...
3
votes
1answer
133 views

SABR calibration: simple explanation and implementation

I would like to learn more about the SABR model and ho it is used in modeling smiles in equity, FX and rates markets. How would you explain the process and its implementation in simple steps? Any web ...
2
votes
1answer
99 views

How literature come up with risk-neutrality problem, considering that market is not really risk-neutral?

I am searching on real-option pricing deficiencies to encounter risk-neutrality. As we know risk-neutrality assumption, is not hold in real situations. The problem is that I could not classified ...
0
votes
1answer
96 views

What is the formula for beta weighted delta and gamma?

I am trying to calculate the beta weighted delta and gamma for a portfolio of options of different underlying stocks, but I can't seem to find the correct formula. Can someone point me to it or a ...
1
vote
3answers
151 views

What is the name of this product?

Consider the payoff =$S_T1_{S_T>K}$ where $S_T$ is the asset price at maturity. What is this type derivative called? and is it a liquid option?
4
votes
1answer
271 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. ...
0
votes
1answer
48 views

how to use known premium of options to determine premium of options with another strike?

Assuming constant volatility across all strikes, how to use known premium of options to determine premium of options with another strike? e.g. suppose we know premium of \$40 call and put, \$50 call ...
0
votes
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
vote
2answers
89 views

Can we trade option spreads with more than 4 option legs?

I am wondering why most online brokers restrict multi-legged options spread trades to have a maximum of four legs? Also, is there a broker that allows you to trade say 6 or 8 legged option spreads.
0
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2answers
152 views

Daily option data

I am wondering where I can pull daily (hourly, by-the-minute, etc. even better) option data for a particular underlying. I would prefer a database I could scrape through and API, but would not mind ...