Title: Combining Monte-Carlo Simulations and Options to manage Risk of Real Estate Portfolios
1Combining Monte-Carlo Simulations and Options to
manage Risk of Real Estate Portfolios
- Amédée-Manesme Charles-Olivier, BNP Paribas Real
Estate Investment Services - Baroni Michel, Essec Business School
- Barthélémy Fabrice, THEMA, University of
Cergy-Pontoise - Dupuy Etienne, BNP Paribas Real Estate Investment
Services
2Research overview
- Objective Taking real estate risk into account,
in particular the risk inherent in the (European)
lease structures - Methodology Combination of Monte-Carlo
simulations and option theory - Conclusion The approach allows a better
Portfolio valuation and numerous and nurturing
risk measurements
3Literature
- Pyhhr, S.A., 1973
- French, N. and Gabrielli, L., 2005
- Hoesli, M., Jani, E. and Bender, A., 2006
- Kelliher, C.F. and Mahoney, L.S., 2000
- Baroni, M., Barthélémy, F. and Mokrane, M., 2001
2007a 2007b - Dupuy, E., 2003 2004
- Barthélémy, F. and Prigent, J-L., 2009
4Continental Europe lease contract the structure
- Lease structures vary across countries
- Long lease (5 to 10 years)
- Usually tenants have options to leave during the
course of the lease Break-Option BO - At the time of a Break-Option the tenant has two
possibilities - Staying
- Leaving
- At the time of a Break-Option the Landlord has no
decision to take but can enter a negotiation
5Continental Europe lease contract the rent
- In Europe,
- Rents usually indexed
- Inflation
- Country specific index
- Fixed indexation
6European Lease contract Risk
- Traditionally, tenants cannot negotiate the rent
during the course of the contract whatever is the
level of the Market rental value.
7Taking lease structure risk and global systematic
risk into accountMonte-Carlo Options
8Simulation of the Price Market Rental Values (I)
9Break-Option Analogy with options theory (I)
- The owner of a call option has the right but not
the obligation to buy an underlying asset at a
predefined price K
- The tenant of a European lease contract is the
owner of an option at the time of a break
option, a tenant has the right but not the
obligation to terminate the lease
vs
10Break-Option Analogy with options theory (II)
- A rational player will exercise its option at
maturity as soon as it is in the money - St gt K
- The value of a European call at maturity is
- A rational tenant will exercise its option to
leave as soon as it is in the money - Rt gt MRVt
- By analogy, the value of a BO can be written
gt
11MRV Tc gt MRVt
12Option should be exercised
13In our implementation
-
- The tenant vacates and the landlord has to find
another tenant for a new rent. Given the
necessary time to find a new tenant, the possible
advantageous financial conditions granted by the
landlord and the state of the market a void
period corresponding to one year is applied in
the cash-flow. -
- The tenant stays in the premises (same rent).
-
- The tenants rent stands between the Market
Rental Value and the Market Rental Value plus the
transaction costs in this case we consider both
the tenant and the landlord adopt a rational
behaviour and start negotiating. For
simplification we consider they will concord to
the market rental value.
14The Model
15The Model
16Net operating income with our model for one
scenario
17Hypothesis of the implementation
18Sensitivities Level of inflows
19Sensitivities Level of inflows
20Sensitivities Valuation of the Portfolio
21Questions?
22European Lease contract Risk
- For the owners, risk concentrated in the lease
structure - The inflows received are based on the rents
indexed and not on the market rental values, the
rents can be overvalued or undervalued - A fixed 10 year lease is safer than a 10 years
lease with an option to break at the fifth year. - Likely to cause vacancy ? Risk
23Monte-Carlo Methods
- averaging results from a large number of samples
to provide meaningful results - Sampling a universe of possible outcomes.
- Require computational implementation
- Monte Carlo methods are based on the analogy
between probability and volume. - Useful when significant uncertainty in inputs
- Useful for risk analysis (reliable and rational)
24Monte-Carlo methods
- Estimate the inputs
- Generate random numbers
- Perform a deterministic computation
- Aggregate the results of the scenario into a
final result - Repeat the last two steps several times
- Aggregate the results
25Simulation of the Price Market Rental Values
(II)
Together correlated with a fixed correlation
parameter
26MRV gt Rt
27BO should be exercised
28European Lease Option
- We do not need to value the premium of the option
- We only need to estimate if the option will be
exercised or not - Therefore at the time of a break-option each
simulated Market Rental Value will be compared to
the rents and the best tenants rational decision
will be taken