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Questions tagged [implied-volatility]

The volatility of the price of the underlying security that is implied by the market price of an option based on an option pricing model.

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Transforming 3M volatilities into 6M volatilities in EUR forecast curves

I have implemented a stripping algorithm to extract forward volatilities from cap/floor flat volatilities for different currencies. I am however struggling a bit when implementing a method to convert ...
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157 views

Jim Gatheral's ansatz

In the Ansatz section of Jim Gatheral's book Volatility Surface (page 32), he assumes $$\mathbb E[x_s|x_T]=x_T\frac{\hat w_s}{\hat w_T}$$ where $\hat w_t:=\int_0^t \hat v_s ds$ is the expected total ...
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590 views

compute time from FX forward, how use DEPO rates?

assume I have following delta-term vol data from broker: ...
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231 views

implied volatility and strike price

Assume for simplicity that the expiration time of an option is $1$ the initial stock price is $1$ and there is no dividend yield and the risk free return is $0$. How is it possible to show that the ...
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98 views

Arbitrage free smoothing of volatility smile - cubic spline - implementation procedure

I am studying the paper Arbitrage-Free Smoothing of the Implied Volatility Surface, from Matthias R. Fengler (https://core.ac.uk/download/pdf/6978470.pdf). The problem I want to solve is much simpler ...
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186 views

Quantitative approaches to measuring the effectiveness of a Stock Option Pricing Model?

My question contains many parts, but I will try to keep it somewhat focused. I am primarily looking for a framework to evaluate the accuracy of a stock-focused Options Pricing Model. One of the ...
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204 views

How companies choose earnings release dates, & effect on Implied Volatility

A company's earnings release date significantly affects weekly or monthly option prices/implied volatility. For companies that typically release earnings on the cusp of monthly options expiration, ...
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85 views

No arbitrage conditions for normal implied volatility

usually the term implied volatility refers to Black-Scholes implied volatility (also Log-Normal volatility): it is defined as a quantity which when plugged in the Black-Scholes formula returns the ...
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54 views

Equity Options - “How do I build a forward simulation model with regards to shocks in spot pricing and IV?”

I am trying to build a "What-If" Portfolio, consisting of a total of 20 options, across different tenors, strikes (delta), but on the same security. Simply put, the objective is for me to test the ...
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314 views

(C++) Monte Carlo pricer for SABR model to test Hagan / Paulot formulas

I'm trying to test the so-called Hagan formula (p.6 of this paper) and the Paulot formula, order 1 only (eq. (43) p.19 of this paper. For this, i'm trying to use both Euler and Milstein scheme ...
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230 views

What is the longest number of consecutive days that options implied volatility has stayed “extremely high” for any particular underlying?

Curious as to whether or not there is any sort of all time record. Any index, future, or stock will do. Volatility must be well above the average 1 year volatility for all periods.
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35 views

Volatility surface fitting, interpolation and extension from sparse data

There are some nice papers about constrained spline fitting essentially giving you a smoothing and arb free surface. I am focusing on the oil market here: The market is essentially split in a very ...
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64 views

Expected VIX at different levels of SPX

I'm looking for a model that computes the expected VIX based on SPX price moves. For instance, SPX is currently at around 2650, and VIX is at 24. If SPX jumps to 2600, at what level would the VIX be? ...
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270 views

American Vs European Options behavior with fixed strikes and varying expiration

Following is from page 10 of Fengler (2005), "The prices of American calls for the same strikes must be nondecreasing, Merton (1973), and in the absence of dividends, this property translates to ...
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142 views

Relationship between Implied Volatility Curve Derivatives and the Underlying's Moments

Very probably this question has been posed before, so if someone can pose the link to the relevant question, it would be appreciated. What is the relationship between the implied volatility skew and ...
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129 views

Implied Equity Volatility under Stochastic Interest Rate

I would like to draw some general conclusions for the effect of stochasticity of interest rate on the implied volatility of a European call of a stock. Below I show, trivially, the implied volatility ...
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37 views

FX Implied Volatility for Longer Term Maturities

To my knowledge, FX implied volatility can only be obtained from the market for time horizons up to about 5 years due to liquidity limitations. So how would we obtain volatility estimates for longer ...
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2k views

Implied volatility from American options using python

I am currently trying to construct volatility surface from american option prices (using Cox-Ross-Rubinstein tree) in Python 2.7. Below you can find the code I came up with. Any corrections would be ...
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1k 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 ...
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73 views

Discount of Asian vs European vols

I understand the discount for Asian vs. European vol depends on time to expiry and length of averaging period. This makes sense intuitively; a short averaging period far away blurs into a single ...
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138 views

What is the relation between return volatility and return rank volatility, and how can I control the latter?

I have no experience in finance, but I've been playing around with a virtual portfolio. I'm trying to control the "rank volatility" distribution - that is, the volatility of a stock's daily rank in ...
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46 views

Black-Scholes IV from Characteristic Function

I'm trying to follow Gatheral 2006 on his derivation of the BSIV from a characteristic function. The most relevant formula is (5.7) page 60. $$\int_0^\infty\frac{du}{u^2+(1/4)}\Re[e^{-iuk}\left(\...
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183 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 (...
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American options — doing better than Black's approximation when $r = 0$

I am trying to find the implied volatility smile for an American call option with a known dividend during the option tenor. For the sake of argument, let's say today is Jan 1, the dividend $D$ is paid ...
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178 views

Expected profit from straddle and its standard deviation

I was reading "Paul Wilmott introduces quantitative finance". In chapter 10 page 227 he states that: If you buy an at-the-money straddle close to expiry the profit you expect to make from this ...
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197 views

Building implied binomial tree with American input options

i want to build an implied volatility binomial tree with American input options, so the setup is the following: 1) We know the market Price P of the American Put $P_{am}(t_i,K)$, where $t_i$ is the ...
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92 views

from local volatility function to implied volatility for a given strike

Assuming we know the local volatility function σ(S,t) for all S and t, how can we recover the corresponding implied volatility for a given strike K (and the other necessary parameters, S, r, T, t...)? ...
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78 views

Implied volatility

I have a question about calculating the implied vol. Assuming the implied vol that a option will expire in 1 day is $\sigma_1$, and the implied vol that the option will expire in 2 days is $\sigma_2$. ...
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93 views

Inverse Smile Volatility Ibex35

I was analysing ibex implied volatility and when I draw it I found it was reversed: X axis are the strikes and Y axis implied volatilities calculated by BS. The blue line is the spot price. Data (...
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286 views

Vol surface changes as underlying moves

We market make in highly liquid, near term options markets. I want to build a risk report that tells us how our portfolio's greeks will change as the underlying moves. This is for risk management in ...
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0answers
280 views

Weighted average implied optionlet/swaptions volatility

Let an implied volatility curve/surface is made up by optionlets or swaptions Black's implied volatility. If you wanted to price, say, a FRN with cap and/or floor, a CMS et cetera you would input the ...
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51 views

How to price equity options using a Black76 implied volatility surface?

I would like to calculate the fair value of american and european options on various equities and indices using QuantLib C++. Since I do have discrete dividends available for most underlyings, I use <...
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39 views

Wrong understanding of implied vol cannot be linear interpolated

There is a well known conclusion that implied vol cannot be linear interpolated. But I am not sure this interpolation is for ...
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51 views

Effect of Volatility Regime on Volatility Smile

For short-term FX options, I find empirically that the degree of curvature of the smile (OTM/ATM in %) is higher in low volatility environments. Similar results are found by Pena et al. ("Why do we ...
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66 views

Vega with SVI Gatheral bumps

How would one go about computing a vega profile of an exotic derivative where the volatility surface is modeled using Gatheral's SVI parameterization? In particular, I am thinking about bumping each ...
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65 views

Local variance derivation by Gatheral

I've bought Gatheral's book on Local Volatility and I have troubles with understanding a part where he shows that local variance is a conditional expectation of instantaneous variance. Why in the ...
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0answers
73 views

Implied Volatility of cross currency pairs

Been looking for this... Is there any way we can infer directly, say GBP-JPY's 1-year volatility from GBP-USD's and USD-JPY's? Many thanks.
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Research topic on volatility

Currently studying about volatility, VIX and implied volatility as well as option pricing via stochastic volatility models. My question is how these are used in real life except of speculation. Do ...
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45 views

Why hasn't SVXY recouped more of its lost value as vol has crashed in the past 2 weeks?

SVXY fell from around \$140 to \$9. It has since bounced back 25% to around \$12. Vix futures went from the 11-14 range to 35 and now back to 17-18. SVXY holds a short position in Vix futures with ...
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82 views

Jim Gatheral's claim on the decay of the effect of jumps on the final return distribution

I got a full answer for my question on Jim Gatheral's book The Volatility Surface. I am going to try my luck again on another question on the same book. In Section The Decay of Skew Due to Jumps on ...
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83 views

Should I interpolate before or after to find option price using Vanna-Volga method?

I am trying to calculate the implied option premium $C(K)$ and $\Delta$ using the procedure outlined by Castagna and Mercurio in this paper - http://www.fabiomercurio.it/consistentfxsmile.pdf My ...
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311 views

Absolute or relative strikes?

World, When pricing a CMS Spread Option the market practice consider the strike as relative to ATM or Absolute? If I relate to the following paper page 70 the author refers to absolute strike [1] ...
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0answers
112 views

Multi objective optimization Swaption/Caplets joint Calibration

People suppose that we have a two asset type portfolio optimization (as Intrument Type 1 and 2). In the each portfolio refered by the instrument type there are 2 asset so we have four asset in total. ...
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107 views

What is relation between option adjusted duration and volatility

I am calculating oasd using implied vol of 15%. What is relation between OASD vs Implied volatility in theory for various maturities. I am running using MMD curve. If anyone recommend any good ...
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0answers
100 views

Is it possible to calculate implied probability of >=X% return based on implied volatilities from options

My question is: Is it possible to imply either the upside or downside (one sided) probability from looking at implied volatilities of stock options? Let's take an example: say you had Stock A at $50, ...
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0answers
479 views

ATM-implied volatility

I am trying to understand the methodology that researchers used to compute ATM-implied volatility with real data. The problem is giving the discrete sets strike prices of one particular option with ...
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0answers
147 views

CDO Implied correlation: what for?

Reading about CDOs and calibration to find the implied correlation, I came up with the following question. Suppose we are pricing a CDO over a pool of $N=125$ names, using the usual Gaussian copula ...
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99 views

IV surface quoted Skew/Curtosis/Putwing/CallWing

I came across a volatility surface quoted in unknown format to me. I have ATM Vol Skew Kurtosis PutWing and CallWing each for particular tenor. Any idea of what these represent/...
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213 views

The name conventions such as ATM, Risk reversal and Butterflies to construct volatility surface

Why people call (vol call - vol put) risk reversal when risk reversal actually is (call 25 delta -put detlta +25)? when constructing volatility surface? The vol of risk revesal should not be vol call -...
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110 views

How can we observe volatility smile from the market. Drawbacks of Heston Stochastic Volatility Model

Here are two questions related to implied volatilities. a) The set up here is for an European option. We can get its implied volatility smile from calibration, the question is why could we also ...