Agency Costs, Risk Management, and Capital Structure

Although property markets represent a large proportion of total wealth in developed countries, the real-estate derivatives markets are still lagging behind in volume of trading and liquidity. Over the last few years there has been increased activity in developing derivative instruments that can be utilised by asset managers. In this paper, we discuss the problems encountered when using property derivatives for managing European real-estate risk. We also consider a special class of structured interest rate swaps that have embedded real-estate risk and propose a more efficient way to tailor these swaps.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1448844_code223089.pdf?abstractid=1448844&rulid=5477143&mirid=5

Property Derivatives for Managing European Real-Estate Risk

/pdf/property-derivatives-for-managing-european-real-estate-risk-1863jk0ixr.pdf

New methods are developed here for pricing the main real estate derivatives — futures and forward contracts, total return swaps, and options. Accounting for the incompleteness of this market, a suitable modelling framework is outlined that can produce exact formulae, assuming that the market price of risk is known. This framework can accommodate econometric properties of real estate indices such as predictability due to autocorrelations. The term structure of the market price of risk is calibrated from futures market prices on the Investment Property Databank index. The evolution of the market price of risk associated with all five futures curves during 2009 is discussed.

https://papers.ssrn.com/sol3/Delivery.cfm/j_1468-036X_2011_00635_x_wml.pdf?abstractid=2164035&mirid=2

A Pricing Framework for Real Estate Derivatives

In Foreign Exchange Markets Compound options (options on options) are traded frequently. Instalment options generalize the concept of Compound options as they allow the holder to prolong a Vanilla Call or Put option by paying instalments of a discrete payment plan. We derive a closed-form solution to the value of such an option in the Black-Scholes model and prove that the limiting case of an Instalment option with a continuous payment plan is equivalent to a portfolio consisting of a European Vanilla option and an American Put on this Vanilla option with a time-dependent strike.

/pdf/instalment-options-a-closed-form-solution-and-the-limiting-29wsvbn382.pdf

Instalment Options: A Closed-Form Solution and the Limiting Case

We present three approaches to value American continuous-installment options written on assets without dividends or with continuous dividend yield. In an American continuous-installment option, the premium is paid continuously instead of up-front. At or before maturity, the holder may terminate payments by either exercising the option or stopping the option contract. Under the usual assumptions, we are able to construct an instantaneous riskless dynamic hedging portfolio and derive an inhomogeneous Black--Scholes partial differential equation for the initial value of this option. This key result allows us to derive valuation formulas for American continuous-installment options using the integral representation method and consequently to obtain closed-form formulas by approximating the optimal stopping and exercise boundaries as multipiece exponential functions. This process is compared to the finite difference method to solve the inhomogeneous Black--Scholes PDE and a Monte Carlo approach.

/pdf/valuation-of-american-continuous-installment-options-3w70041yb4.pdf

Valuation of American Continuous-Installment Options

A model for pricing real estate derivatives with stochastic interest rates

A perpetual continuous-installment option is an infinite maturity option in which the premium is paid continuously instead of upfront. The holder has the right to terminate payments at any time by either exercising the option or dropping the option contract. Within the standard Black-Scholes framework, the perpetual continuous-installment option pricing problem is discussed and solved as a free boundary problem for a parabolic inhomogeneous ordinary differential equation. The closed-form solution obtained for the special case of a non-dividend paying asset gives the possibility to observe some analytical properties of the initial premium and the optimal boundaries for the perpetual continuousinstallment call option.

A note on the pricing of perpetual continuous-installment options

This paper is concerned with the valuation of European continuous-installment options where the aim is to determine the initial premium given a constant installment payment plan. The distinctive feature of this pricing problem is the determination, along with the initial premium, of an optimal stopping boundary since the option holder has the right to stop making installment payments at any time before maturity. Given that the initial premium function of this option is governed by an inhomogeneous Black-Scholes partial differential equation, we can obtain two alternative characterizations of the European continuous-installment option pricing problem, for which no closed-form solution is available. First, we formulate the pricing problem as a free boundary problem and using the integral representation method, we derive integral expressions for both the initial premium and the optimal stopping boundary. Next, we use the linear complementarity formulation of the pricing problem for determining the initial premium and the early stopping curve implicitly with a finite difference scheme. Finally, the pricing problem is posed as an optimal stopping problem and then implemented by a Monte Carlo approach.

Valuation of European continuous-installment options

In this paper we present an integral equation approach for the
valuation of European-style installment derivatives when the payment
plan is assumed to be a continuous function of the asset price and
time. The contribution of this study is threefold. First, we show
that in the Black-Scholes model the option pricing problem can be
formulated as a free boundary problem under very general conditions
on payoff structure and payment schedule. Second, by applying a
Fourier transform-based solution technique, we derive a recursive
integral equation for the free boundary along with an analytic
representation of the option price. Third, based on these results,
we propose a unified framework which generalizes the existing
methods and is capable of dealing with a wide range of monotonic
payoff functions and continuous payment plans. Finally, by using the
illustrative example of European vanilla installment call options,
an explicit pricing formula is obtained for time-varying payment
schedules.

Pierangelo Ciurlia

Papers

Valuation of American Continuous-Installment Options

A model for pricing real estate derivatives with stochastic interest rates

A note on the pricing of perpetual continuous-installment options

Valuation of European continuous-installment options

On a general class of free boundary problems for European-style installment options with continuous payment plan