Questions tagged [put-call-parity]
The put-call-parity tag has no usage guidance.
84
questions
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Forward Index Level in VIX calculation
The VIX white paper (https://cdn.cboe.com/resources/vix/vixwhite.pdf) step #1 (page 6) says the the Forward Index Price is calculated as:
F = Strike Price + e^RT x (Call Price - Put Price).
Why doesn'...
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0answers
61 views
VIX options underlying: Can I safely use Put-Call parity instead of VIX futures
Couple of basic questions:
1- I'd like to calculate the implied of VIX options intraday, without access to intraday VIX futures.
In the absence of VIX futures as underlyings, what would be the ...
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0answers
58 views
calculating risk free interest rate from put call parity
I'm trying to calculate the interest rate $r$ from the put-call parity.
As per hull, put-call parity is given by the below equation.
$c + Ke^{-rT} = p + S_{0}$
where:
$c$ = current call option price ...
1
vote
2answers
554 views
How to prove no-arbitrage when a long butterfly is strictly positive?
I want to prove why there are no arbitrage opportunities when a long butterfly is strictly positive. I know there is a similar topic out there, but it seems it doesn't solve my question: Prove that ...
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0answers
25 views
How do borrow rates in single-stock options affect their prices
Would following approach be suitable:
First calculate European option price (does it even make sense to do so, if we are talking about less than 30 dte?), take the diff between European and American ...
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1answer
108 views
Put-Call Parity with dividends
In which book will I find the exact proof of put-call parity in the case when asset pays continuous dividend? I need a book to cite this result
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0answers
45 views
How to Show an Arbitrage Opportunity Exist From a Market-Linked CD?
A bank issues a market-linked CD that guarantees the original principal with an interest at an effective annual rate of 2%, plus 70% of the percentage gain on the ABC Inc. non-dividend-paying stock ...
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0answers
47 views
Put-call parity under a regime-switching model
I need some help.
I'm given $J$ different regimes, each one characterized by its own parameters $(r_i, \delta_i,\sigma_i,...)$ with $i\in \mathcal{J}= \{1,2,...,J\}$ ($r$ = risk-free interest rate, $...
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34 views
Why is the correlation that Futures Options have with interest rates opposite to that of the one Stock Options have?
The Put-Call Parity relationship for Stock Options is the following:
Call Price - Put Price = Stock Price - Exercise Price + Carrying Costs - Dividends
But for Options on Futures where the Options ...
4
votes
1answer
221 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 ...
1
vote
1answer
206 views
Under Put-Call Parity, why do we add the cost of carry to Call prices but subtract them from the Stock price and Put prices?
In Natenberg (1994) Chapter 11 he outlines the Put-Call parity relationships.
...
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43 views
The wider bid-ask spread of in-the-forward American option
Why is the bid-ask spread of a in-the-forward/money American call (put) much larger than the out-of-the-forward/money American put (call)? I suppose the answer to the same corresponding question ...
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0answers
42 views
Black-Scholes pricing of european call option
I am really confused on the usage of the greeks and the Black-Scholes model for option pricing. To gain some more understanding I am attempting to see if I can price a european call option under the ...
1
vote
3answers
80 views
Equivalent combination of puts
Suppose that a certain stock is currently worth $S_0=\$61$. Consider an investor that buys
one call with a strike price equal to $K_1=\$55$, that costs $c_1=\$10$, buys another call with strike
price ...
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0answers
18 views
Insured Portfolio via call + cash: how much cash?
I am unsure about the quantities to keep in the risky asset, S, and the non-risky asset, M, when constructing an insured portfolio via Call + Cash (rather than Stock + Put). My understanding so far is ...
1
vote
1answer
100 views
Put-Call parity arbitrage relationship
I would like to know what the relationship is between the time value of call/puts. From the put call parity formula
$$C-P = S_{t} - PV(K)$$
and that value of call/put options is simply the sum of ...
0
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1answer
235 views
Calculating risk free rates from risky options using put call parity
My questions relates to this post Implying risk-free rates using Put/Call parity , but I am using a different approach.
Given: ODAX (Options on "DAX") Settlement prices across different maturities ...
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1answer
369 views
Calculate forward price based on option chain
I've got historical data for a spy option chain which looks as follows
...
2
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1answer
236 views
Boundary for European Put Option
As an entry level financial engineer, I'm learning about call-put parity, which helps us to get the boundary for call option: $S-Ke^{-rT}\leq c\leq S$, what about put option? Should its upper bound be ...
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0answers
38 views
What is the effect of put call open Interest on price action
how option put call open Interest affects price actions as put sellers feel price when price goes down or call sellers feel pain when price goes up and how this affects price action. ie when price ...
1
vote
1answer
2k views
Proving the put call parity
In my course notes on the put-call parity, the proof is presented by going over two inequalities, namely $\text{RHS} > \text{LHS}$ implies arbtirage and $\text{RHS} < \text{LHS}$ implies ...
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2answers
159 views
Why are put and call options worth the same despite that put has no upside whereas call has unlimited upsides?
The following is an interview question.
All Black-Scholes assumptions hold. Assume no dividends. Consider a standard European call and a standard European put on the same stock. Assume that each ...
0
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1answer
70 views
Time to Put or Call a Bond
I was studying putable bond and callable bond on my own, there is an exercise question that was a little confusing to me:
I understand what the answer explains, but I am confused that, is a bond "...
1
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1answer
293 views
Continuous Geometric Asian Options
Assume the risk-free bond $B_t$ and the stock $S_t$ follow the dynamics of the Black & Scholes model
without dividends (with interest rate r, stock drift $\mu$ and volatility $\sigma$).
Let $c(t; ...
2
votes
1answer
202 views
How to prove Gamma is the same for a European call and European put with the same inputs?
I saw from a text "From put-call parity, call and put with the same inputs have the same gamma", but I don't see how put-call parity is related to Gamma. Can someone explain? Thanks!
2
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1answer
248 views
Why is put-call parity defined differently by CME and Wikipedia?
In general, Wikipedia defines Put-Call parity as:
C - P = D(F - K)
----------------
C = call price
P = put price
F = *FORWARD* price
K = strike
which can be re-...
1
vote
0answers
76 views
Prove the following Call and Put relationship: [duplicate]
I need to prove that
$$c(S,X,T)=\frac{X}{F}p(S,\frac{F^2}{X},T)$$
where
$$F=Se^{(r-q)(T-t)}$$
I am having trouble proving this relationship. Is this relationship even possible? If so, can someone ...
0
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0answers
43 views
Put-call parity for equity share and debt share
Considering Merton's structural approach" for credit risk modeling, we arrive to prove that the pricing formules are $S_t=V_t\phi(d_{T,1})-Fe^{-r(T-t)}\phi(d_{T,2})$ for equity share and $F_t=FP_0(t,T)...
1
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1answer
67 views
Why do we need to borrow money in the call-put parity? [closed]
As I understand it, the call put parity is given by
$$c = p + S - \frac{X}{(1 + r)^T}$$
I understand the rationale behind simultaneously buying the call, put and underlying asset for $S$, but why ...
3
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0answers
311 views
What are the main problems for calculating the implied volatility of in the money American put options?
As stated in the question I have a problem with calculating the implied volatility for in the money put options I have a data set of 2.6 million American style plain-vanilla call and put options. For ...
6
votes
2answers
292 views
Why do I get a curved line when I plot “implied interest rate” on the strike price?
Currently, I am working on my thesis (MSc. Finance) and I run into an interesting “phenomenon”. I have option data for a non-dividend paying stock. In class I have learned, how to calculate the ...
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0answers
96 views
Is it necessary for $P(K, t) - P(K + s, t) \geq se^{-rt}$ to hold?
Let $P(K, t)$ be a put option with strike price $K$ and expiration time $t$. Let $s > 0$. Is it necessarily true that the inequality
$$P(K, t) - P(K + s, t) \geq se^{-rt}$$
holds? I know that ...
0
votes
1answer
127 views
How to get Forward price based on Put-Call parity?
Could you advise how to find a forward price using Call/Put (+Spot and Strike) ? Investodepia says that forward is equal to option's strike based on Put-Call Parity but it seems to me there is a ...
1
vote
1answer
559 views
Bermudan Swaption
Is there an equation of the kind of call-put parity for Bermudean swaptions ? (maybe an inequality )
Is there an intuitive description of what would be an optimal exercise moment ? Intuitively I ...
0
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2answers
127 views
Construct a portfolio of European call options with a certain payoff function
My question is similar to Replicate a Portfolio with Given Payoff but I am not quite sure how to apply this to my problem.
A portfolio of European call options on an asset $S_T$ has a payoff function ...
2
votes
1answer
229 views
Determine the maximum arbitrage profit from the given contracts
I really have tough time trying to figure this out.
An investor observes the following prices in the market: Euro-Stoxx-Future DEC 148.02-148.03; Euro-Stoxx-Future Call-Option DEC 148.00 1.13-1.15; ...
5
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0answers
296 views
Implied Funding/Borrow Costs in Short-Dated ETF Option Prices
I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
2
votes
1answer
251 views
Should Put/Call Parity result in Zero Return or the Risk-Free Rate?
Sorry in advance if this is a basic question. I'm examining some potential at-the-money put/call arbitrage. What I found surprised me somewhat:
...
2
votes
1answer
413 views
Call Option Overvalued and put-call parity [closed]
I have a question regarding if a Call option is overvalued compared to the call price and how you can benefit from the Arbitrage opportunity.
My thoughts are as follows:
Step 1: Short the call ...
1
vote
1answer
142 views
Is there an advantage trading options based on deep in the money Open Interest Volume ratio
Problem:
Deep in the money options contracts will be assigned at expiration date.
Higher Volume ratio of deep in the money contracts at expiration calls or puts leads to day after expiration date we ...
0
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1answer
222 views
Decreasing value of the Put option with increasing Time to maturity [closed]
Can you think of a situation when increasing the time to maturity lowers the value of a put option? If yes, show the example pls.
2
votes
1answer
194 views
Risk of Put-Call-Parity in practice
When $C+PV(K) \ne P + S_0$, it's an opportunity for risk-free arbitrage (excluding cost).
In practice, what potential risk could make the arbitrage fail?
I know that failure to build complete ...
1
vote
1answer
142 views
Equity repo close to money market rates?
I've noticed that the repo rate (here I mean the effective financing rate of the forward position in stock) implied from synthetic forwards is almost the same as money market benchmark (XXXibor 3M) ...
7
votes
2answers
3k views
Put-call parity for cash settled swaptions
The Euro swaption market is changing from cash to physical settlement quotation in July 2018 $-$ see e.g. "Euro swaptions market prepares for pricign revamp (Risk, 2018)". When describing ...
2
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3answers
1k views
Put Call Symmetry
I want to show the Put Call Symmetry without using the explicite Black Scholes formula. In other words I want to show
Call(t, x, K, T) = Pull(t, K, x, T)
where $S_t = x $ for $t \in [0, T]$.
I ...
0
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0answers
78 views
Different versions of Put-Call Parity
Why is it stated sometimes that $C - P = F$
and in wikipedia it statest that $C - P = D(F-K)$, where D is the discount factor and K is the strike (of both the call and put?).
Is this just affected ...
3
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0answers
671 views
Understanding put-call parity
I'm a person with math background trying to break into quantitative finance, and there's something about put-call parity that is not making sense to me. Below I'll detail my understanding of the ...
5
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1answer
492 views
Interpretation and intuition behind the Put-Call symmetry under the Heston Model
I am currently working on a report regarding the put-call symmetry relations under the Heston model. I did all the math and managed to prove the relations using PDE approach. However, I wish to have a ...
3
votes
1answer
627 views
Question about the vega of a stock
In Black-Scholes model with constant parameters, a call and a put with the same characteristics have the same vega: https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model#The_Greeks
Using call-put ...
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0answers
384 views
Convexity of Call option prices using Put-Call parity relationship
I am trying to price vanilla options using a particular Bayesian approach that I have found in a paper. To do that I need to construct a likelihood function, approximating the tail of the distribution ...
