# Questions tagged [put-call-parity]

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### Setting the r in put-call parity?

Put-call parity is given by $C + Ke^{-r(T-t)} = P + S$. The variables $C$, $P$ and $S$ are directly observable in the market place. $T-t$ follows by the contract specification. The variable $r$ is ...
4k views

### Why the interest rate for put-call parity is not constant?

Usimg the put-call parity $C - P = S - K · e^{-rt}$ I tried to estimate the value of $e^{-rt}$, the present value of a zero-coupon bond that matures to 1 in time $t$: $e^{-rt} = (P - C + S) / K$ ...
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### Implying risk-free rates using Put/Call parity

I recently purchased SPX options data from the CBOE. Normally, if the data is OK and the Put-Call parity holds, one should expect to correctly imply ZC (Zero Coupon bond) prices and forwards by ...
807 views

### What changes to put-call parity are necessary when evaluating american options on non-dividend paying assets?

If an underlying doesn't pay dividends (for our purpose defined as any distribution to the underlying's holder) directly or indirectly (e.g. options on futures) how does put-call parity change from ...
9k 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 ...
2k 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 ...
1k views

### At the money put and call having the same price

This is a commonly asked question and I have not been able to find a satisfactory answer to it. Let me first phrase it here. Suppose that interest rates are $0$ and consider an at the money put and an ...
240 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 ...
6k views

### Relationship between forward and option prices

Do forward prices factor into option prices at all? It seems to me from Black-Scholes that you just need a spot price and interest rate r. I understand that $F_t = S_0 e^{r t}$, but I don't know if ...
3k views

### Difficulty understanding put-call parity for currency options

I am self-studying for an actuarial exam on models for financial economics. I am having difficulty thinking about the put-call parity for currency options, specifically how use the notation. Here is ...
214 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 ...
12k views

### Early execise of American Call on Non-Dividend paying stock.

Let us consider an American call option with strike price K and the time to maturity be T. Assume that the underlying stock does not pay any dividend. Let the price of this call option is C$^a$ today ...
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### 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 ...
905 views

### Does put-call parity hold for a compound option with underlying American option?

Say there is an American put option that expires $N$ months from today. A call-on-put (CoP) option provides the owner the right to buy the American put option in exactly $M < N$ months (but no ...
999 views

### Build a Synthetic Loan for Personal Finance

Suppose I am short of cash and want a loan for some mundane objective like travelling or buying a car. The interest rate for personal loan with my bank is too high. Is there any way in finance that ...
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### put-call parity equation

I'm reading this book and I'm looking at page 4, and we are considering the case where $C_t - P_t - S_t$ is negative, which means that selling the call did not offset the cost of the stock and the put ...
945 views

### Construct option and stock portfolio

If a riskless security costs 100 today and will cost 120 at time T, a stock costs 50 today and will either be 70 or 30 at time T, and call options on the stock have strike price 50 expiring at time T, ...
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### Why is IV different between put and call of same strike

In his book 'Dynamic Hedging' Nassim Taleb says that the volatility of an OTM put should be exactly equal to that of a corresponding in the money call of same strike. But in option chains, the ...
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### 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 ...
545 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 ...
100 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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### 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!
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### 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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### 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: ...
207 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-...
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### 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 ...
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### 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 ...
247 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 ...
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### Understanding the necessary and sufficient conditions for rational early exercise of a call option

I am self-studying for an actuarial exam, and I encountered the following in my text: The author states that if $PV_{t, T}\text{(Divs)} < K(1 - e^{-r(T - t)})$, early exercise is not rational. ...
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### What exactly is the annualized forward premium?

A forward contract has a premium of $0$ because it is an obligation to buy or sell something in the future (hence there is more risk). Call and put options, on the other hand, have premiums of $C$ ...
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### 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; ...
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### Is an options implied dividends DCF model consistent with risk neutral/arbitrage-free valuation?

We're talking about how we price every financial instrument: by discounting the payoff, that is, we take future cash flows and we discount them by a proper rate which takes into account the risk of ...
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### 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 ...
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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 ... 1answer 122 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 ... 3answers 411 views ### Put-Call Parity Application In the binomial model, how that the Delta of a call option$\Delta^{call}$and the Delta of a put option$\Delta^{put}$with the same maturity and strike satisfy $$\Delta^{call}_t - \Delta^{put}_t = ... 1answer 81 views ### Put-Call parity arbitrage relationship I would like to know what the relationship is between the time value of call/puts. From the put call parity formula$$C-P = S_{t} - PV(K)$$and that value of call/put options is simply the sum of ... 1answer 386 views ### Proving the put call parity In my course notes on the put-call parity, the proof is presented by going over two inequalities, namely \text{RHS} > \text{LHS} implies arbtirage and \text{RHS} < \text{LHS} implies ... 1answer 240 views ### Continuous Geometric Asian Options Assume the risk-free bond B_t and the stock S_t follow the dynamics of the Black & Scholes model without dividends (with interest rate r, stock drift \mu and volatility \sigma). Let c(t; ... 1answer 468 views ### Bermudan Swaption Is there an equation of the kind of call-put parity for Bermudean swaptions ? (maybe an inequality ) Is there an intuitive description of what would be an optimal exercise moment ? Intuitively I ... 2answers 635 views ### Prove that the vertical spread condition is bounded I need to prove that vertical spread is bounded, by using no arbitrage condition. 0 > (C(T,K1 )- C(T,K2))/(K1- K2 ) >-e^(-r*T ) I have documented my ... 1answer 235 views ### Is this representation of the put-call parity correct? (Implied dividend estimation) I am looking at implied dividend yields to be obtained from the put-call parity and have come across the following answer: Implied dividend estimation It states that$$ PV(div) = P - C + (S - K) + K(... 1answer 133 views ### Put call parity: when are the premiums the same? Please explain why put call parity could be compared to the payoff of a long forward contract. ie.$C_E-P_E=V_X(0)$where$C_E,P_E$are the call/put premiums and$V_X(0)$is the value of a long ... 1answer 97 views ### What is more likely effect to call and put prices, respectively, if the stock price decreases by$1?

The current stock price is \$80.Call ,and ,put, options, with ,exercise ,prices, of$50 and 3 days to maturity are currently trading. What is more likely effect to call and put prices, respectively, ...
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### 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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### 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 ...
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### 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) ...