Option contracts for a privacy-aware market

Option contracts for a privacy-aware market

Maurizio Naldi Giuseppe D’Acquisto

Universita di Roma “Tor Vergata”

PRINF 2015Dresden · 21 September 2015

Privacy needs

We take care of individuals’ privacy...as consumers......but what about individuals’ privacy as prosumers......and companies’ private data (e.g. their stock level)?

Companies’ private data may be protected when facing the market

Naldi-D’Acquisto (URM) Option contracts PRINF 2015 2 / 15

Privacy needs

We take care of individuals’ privacy...as consumers...

...but what about individuals’ privacy as prosumers...

...and companies’ private data (e.g. their stock level)?



Privacy needs

We take care of individuals’ privacy...as consumers......but what about individuals’ privacy as prosumers...

...and companies’ private data (e.g. their stock level)?



Privacy needs




Privacy needs




Contents

The marketOption contractsOption pricingThe broker’s budget


Contents

The market

Option contractsOption pricingThe broker’s budget


Contents

The marketOption contracts

Option pricingThe broker’s budget


Contents

The marketOption contractsOption pricing

The broker’s budget


Contents

The marketOption contractsOption pricingThe broker’s budget


The market

Customers demand fork∗ itemsThe broker gets all theitems (k ) delivered byprivacy-aware suppliersIf those are not enough,the broker has theremaining (k∗ − k)+

produced

Privacy-aware supplier

Broker

k items(reduced price)

Customers

k* items

Producer(k*-k)+ items

Broker/Producer

The broker pays a fixed price cq for the queryThe broker pays a unit price cp for the items producedThe broker pays a unit price cs < cp for the items delivered byprivacy-aware suppliers


The market


produced


Broker


Customers

k* items


Broker/Producer



The market

Customers demand fork∗ items

The broker gets all theitems (k ) delivered byprivacy-aware suppliersIf those are not enough,the broker has theremaining (k∗ − k)+

produced


Broker


Customers

k* items


Broker/Producer



The market

Customers demand fork∗ itemsThe broker gets all theitems (k ) delivered byprivacy-aware suppliers

If those are not enough,the broker has theremaining (k∗ − k)+

produced


Broker


Customers

k* items


Broker/Producer



The market


produced


Broker


Customers

k* items


Broker/Producer



The market


produced


Broker


Customers

k* items


Broker/Producer

The broker pays a fixed price cq for the query

The broker pays a unit price cp for the items producedThe broker pays a unit price cs < cp for the items delivered byprivacy-aware suppliers


The market


produced


Broker


Customers

k* items


Broker/Producer

The broker pays a fixed price cq for the queryThe broker pays a unit price cp for the items produced

The broker pays a unit price cs < cp for the items delivered byprivacy-aware suppliers


The market


produced


Broker


Customers

k* items


Broker/Producer



Option contracts


Option contracts


Option contracts


Option contracts


Option contracts


Option contracts


Option contracts


Option contracts


The right price

The broker wishes to transfer its risk on the customerThe average extra-payment for the broker is the price tag for thecustomerpopt = Ek

[(k − k∗)+cs|k

]= cs

[(k − k∗)+ + 1

2λe−λ|k−k∗|]

-20 -10 0 10 20Declared excess items

0

5

10

15

20

Opt

ion

pric

e

λ = 0.25λ = 0.5λ = 0.75


The right price

The broker wishes to transfer its risk on the customer

The average extra-payment for the broker is the price tag for thecustomerpopt = Ek

[(k − k∗)+cs|k

]= cs

[(k − k∗)+ + 1



0

5

10

15

20

Opt

ion

pric

e

λ = 0.25λ = 0.5λ = 0.75


The right price

The broker wishes to transfer its risk on the customerThe average extra-payment for the broker is the price tag for thecustomer

popt = Ek

[(k − k∗)+cs|k

]= cs

[(k − k∗)+ + 1



0

5

10

15

20

Opt

ion

pric

e

λ = 0.25λ = 0.5λ = 0.75


The right price


[(k − k∗)+cs|k

]= cs

[(k − k∗)+ + 1



0

5

10

15

20

Opt

ion

pric

e

λ = 0.25λ = 0.5λ = 0.75


The right price


[(k − k∗)+cs|k

]= cs

[(k − k∗)+ + 1



0

5

10

15

20

Opt

ion

pric

e

λ = 0.25λ = 0.5λ = 0.75


Does it pay the broker?









The budget equationB = popt + k∗ · ps − cq − k · cs − (k∗ − k)+cp



The budget equationB = popt + k∗ · ps − cq − k · cs − (k∗ − k)+cp

The minimum price

ps >cq+k ·cs+cp(k∗−k)

+−cs(k−k∗)++(cp−cs)

e−λ|k−k∗|2λ − cp

2 e−λk(k∗+ 1λ)

k∗


Conclusions

A market emerges to protect companies’ data while facing themarketA broker acts as an intermediary between privacy-aware suppliersand customersPrivacy is paid through price reduction by privacy-aware suppliersCustomers benefit from reduced prices but share the risk ofexcess supply through an option contractA pricing formula for the option contract is provided


Conclusions

A market emerges to protect companies’ data while facing themarket

A broker acts as an intermediary between privacy-aware suppliersand customersPrivacy is paid through price reduction by privacy-aware suppliersCustomers benefit from reduced prices but share the risk ofexcess supply through an option contractA pricing formula for the option contract is provided


Conclusions

A market emerges to protect companies’ data while facing themarketA broker acts as an intermediary between privacy-aware suppliersand customers

Privacy is paid through price reduction by privacy-aware suppliersCustomers benefit from reduced prices but share the risk ofexcess supply through an option contractA pricing formula for the option contract is provided


Conclusions

A market emerges to protect companies’ data while facing themarketA broker acts as an intermediary between privacy-aware suppliersand customersPrivacy is paid through price reduction by privacy-aware suppliers

Customers benefit from reduced prices but share the risk ofexcess supply through an option contractA pricing formula for the option contract is provided


Conclusions

A market emerges to protect companies’ data while facing themarketA broker acts as an intermediary between privacy-aware suppliersand customersPrivacy is paid through price reduction by privacy-aware suppliersCustomers benefit from reduced prices but share the risk ofexcess supply through an option contract

A pricing formula for the option contract is provided


Conclusions

A market emerges to protect companies’ data while facing themarketA broker acts as an intermediary between privacy-aware suppliersand customersPrivacy is paid through price reduction by privacy-aware suppliersCustomers benefit from reduced prices but share the risk ofexcess supply through an option contractA pricing formula for the option contract is provided


Option contracts for a privacy-aware market

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