Skip to main content
9 votes

Is it possible to have only one volatility surface for american options (that fits both calls and puts)?

Usually, there is only one vol surface (I have never seen or heard of anyone using two). Almost certainly the most advanced commercially available vol surfaces are built by voladynamics. They also ...
AKdemy's user avatar
  • 9,024
8 votes

Boundary for European Put Option

Let's carefully distinguish which exercise type we consider. European-style call option $$ \max\{S_0-Ke^{-rT},0\}\leq C_E \leq S_0.$$ European-style put option $$\max\{Ke^{-rT}-S_0,0\}\leq P_E\leq ...
Kevin's user avatar
  • 16k
7 votes
Accepted

Interpretation and intuition behind the Put-Call symmetry under the Heston Model

This is a consequence of transforming a Put on $S_T$ with strike $K$ into a Call on $(K S_0)/S_T$ with strike $S_0$ under the stock measure. The new set of parameters $r_p$, $q_p$, $\kappa_p$, ... etc ...
Antoine Conze's user avatar
7 votes

How to prove Gamma is the same for a European call and European put with the same inputs?

Put-call parity says that a call and put (worth $C$ and $P$ respectively) with the same strike $K$ have the following relationship with the spot rate $S$, risk-free rate $r$, and time to maturity $T$ -...
Chris Taylor's user avatar
  • 5,931
6 votes
Accepted

Implying risk-free rates using Put/Call parity

Once upon a time, all option contracts ceased trading on the third Friday of every month. There was no after hours trading for the underlying. When the exchanges closed, everything was done. This ...
Dave Harris's user avatar
  • 4,299
6 votes
Accepted

Violation of the call-put parity

On 10/24/17, Wells Fargo announced that they would pay a dividend of 0.39 to holders of record on 11/3/17. Thus, if you buy the stock after this date (through the exercise of the call) you do not get ...
dm63's user avatar
  • 17.2k
6 votes
Accepted

How does a stock becoming hard to borrow affect puts and calls?

As you described, buying a put and selling a call in the hard to borrow stock, you have created a synthetic short future. Like other equity finance positions, the "difficulty to borrow the stock&...
AlRacoon's user avatar
  • 6,632
6 votes

Proof of the put-call parity formula

There's something wrong with your logic. You assume the formula is correct at time $t$, being today. Then you state that at time $"t=T"$ we must have $X_T = Y_T$. But how did you get that? You ...
dm63's user avatar
  • 17.2k
5 votes
Accepted

Question about the vega of a stock

Vega is the partial derivative of the option price (as a function of parameters -- current stock price $S_t$, strike price $K$, implied volatility $\sigma$, etc.) with respect to $\sigma$ -- holding ...
RRL's user avatar
  • 3,700
5 votes
Accepted

Relationship between forward and option prices

At the heart of the (relative) pricing theory is the concept of no arbitrage and replication. I'll focus on equities here because as stated in the comments it may be more complicated for commodities. ...
Quantuple's user avatar
  • 14.7k
5 votes

Implying risk-free rates using Put/Call parity

Elaborating on my comment: consider a 100 point in the money collar, one day before expiration. You are effectively claiming the price of this is 99.5. But if you call the pit and get a two way ...
dm63's user avatar
  • 17.2k
5 votes
Accepted

Put-Call Parity with dividends

Diviends or not, the put-call parity (with European options) always hold: $ C(S,K) - P(S,K) = F - K*DF $ In the RHS, dividends will impact the forward $F$ (higher dividends imply lower forward). So ...
Soumirai's user avatar
  • 624
5 votes
Accepted

How to prove no-arbitrage when a long butterfly is strictly positive?

I am not sure why the question you link to does not provide an answer. I’ll try to answer it but it is really similar to what has already been said there. Bottom line is: if the value $K$ is reachable ...
Daneel Olivaw's user avatar
5 votes
Accepted

Black and scholes option pricing

Let us start by considering a bear spread strategy, consisting on long a European put with strike $K_2$ and short another European put with strike $K_1$. Then the payoff of this portfolio at expiry $T$...
Daneel Olivaw's user avatar
4 votes
Accepted

Put-Call Parity on Currency and Binomial Trees

You have forgotten the combinatorial factors for binomial probabilities on your terms. You need $$ {n\choose k} p^n(1-p)^{n-k},$$ not just $$ p^n(1-p)^{n-k}.$$ The second term should have a factor of $...
spaceisdarkgreen's user avatar
4 votes
Accepted

Put Call Symmetry

The Black-Scholes symmetry formula is valid only under Black-Scholes as its name suggests. It works only for a lognormal $S$. For other models, you can find symmetry relations but they will be ...
byouness's user avatar
  • 2,230
4 votes
Accepted

Should Put/Call Parity result in Zero Return or the Risk-Free Rate?

You should see the risk free rate as the return on the strategy. That’s because you actually have to invest money , namely usd 19000 minus usd 38, for the one month period. Hence, there is no ...
dm63's user avatar
  • 17.2k
4 votes
Accepted

Put-call parity for cash settled swaptions

The market standard formula approximation for cash settled swaptions applies Black/shifted Black/Bachelier around the forward swap rate so that with this formula parity between payer and receiver ...
Antoine Conze's user avatar
4 votes

Is there an advantage trading options based on deep in the money Open Interest Volume ratio

I don't mean to suggest such a large topic, but it would certainly be worth reading about delta-hedging with regards to your question. Since such a large percentage of options are delta-hedged, the ...
MonteCarloSims's user avatar
4 votes
Accepted

Proving the put call parity

There are usually two ways to write proofs of equalities (like put-call parity) in quantitative finance. By replication, by constructing arbitrage. Both of these are actually the same, since the ...
Stijn D'hondt's user avatar
4 votes

How to prove no-arbitrage when a long butterfly is strictly positive?

as it was stated correctly in the question all long butterfly options have to have a non-negative premium in order for No-arbitrage to hold. So we can say that: No-Arbitrage holds implies All ...
Cettt's user avatar
  • 1,456
4 votes
Accepted

Put Call derivation using two approaches [ Some confusion of getting different results ]

The put-call parity from CME, C - P = F - K, is not correct. I think CME is making it simple. You need to discount the right-hand side. Then, you will get the same ...
jChoi's user avatar
  • 1,174
4 votes
Accepted

Why does the risk-free rate implied by put-call parity vary with strike prices?

I'm pretty sure this is because the options are American. High strike puts are optimal to exercise early, hence the implied discount factor should be closer to 1 on the right hand side.
dm63's user avatar
  • 17.2k
3 votes

Decreasing value of the Put option with increasing Time to maturity

This situation can arise with some non-vanilla options. For example, a digital put option, which pays $1$ if the underlying price $S$ is below a strike $K$ at expiry, can exhibit "negative theta". ...
RRL's user avatar
  • 3,700
3 votes

Risk of Put-Call-Parity in practice

Financing Risk e.g. You sell the stock short and buy the Call and sell the Put. Lets say you can only get a 1w repo borrow on the stock yet your options are 3m options. You have the risk after that ...
Michael T's user avatar
3 votes

Relationship between forward and option prices

In developed equity markets you have at least those three entities: Stocks, futures and options. As far as my experience goes you indeed often hedge options with futures. What is more interesting ...
vonjd's user avatar
  • 27.5k
3 votes
Accepted

At the money put and call having the same price

One thing to notice is that indeed $E^Q[S_T]=S_0$, by construction, even though the stock price can only drop down to 0, but it can go up to $2\,S_0, 3\,S_0, 100\,S_0$, ... Thus, implicitly, there ...
Fab's user avatar
  • 345
3 votes

Bermudan Swaption

There is no put call parity for Bermudan swaptions. There are some necessary (but not sufficient ) conditions for exercise of a Bermudan swaption. For example , consider a Bermudan receiver option ...
dm63's user avatar
  • 17.2k
3 votes
Accepted

Why is put-call parity defined differently by CME and Wikipedia?

There are two ways to look at it, a mathematical way or an alternative, intuitive way. The alternative way can be to look at F as an alternative S with 0 interest rate discounting because we still ...
uday's user avatar
  • 792
3 votes
Accepted

Continuous Geometric Asian Options

Whether arithmetic or geometric averaging, you always get \begin{align*} \mathrm{AsianCall} - \mathrm{AsianPut} = e^{-rT} (\mathbb{E}[\bar{S}]-K). \end{align*} So, let’s compute the expectation. You ...
Kevin's user avatar
  • 16k

Only top scored, non community-wiki answers of a minimum length are eligible